Page 1 TI-82 STATS GRAPHING CALCULATOR GUIDEBOOK © 1996, 2000, 2005 Texas Instruments Incorporated. IBM is a registered trademark of International Business Machines Corporation Macintosh is a registered trademark of Apple Computer, Inc.
Page 2 “as-is” basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or...
Page 3 Table of Contents This manual describes how to use the TI-82 STATS Graphing Calculator. Getting Started is an overview of TI-82 STATS features. Chapter 1 describes how the TI-82 STATS operates. Other chapters describe various interactive features. Chapter 17 shows how to combine these features to solve problems.
Page 4: Table Of Contents
Table of Contents (continued) Chapter 2: Getting Started: Coin Flip ................. Math, Angle, and Keyboard Math Operations ................Test Operations Operations MATH ....................Using the Equation Solver ................(Number) Operations 2-13 MATH NUM .............. Entering and Using Complex Numbers 2-16 ............
Page 5 ....................Using Web Plots to Illustrate Convergence 6-12 ........... Graphing Phase Plots 6-13 ................... Comparing TI-82 STATS and TI.82 Sequence Variables 6-15 ... Keystroke Differences Between TI-82 STATS and TI-82 6-16 ..Chapter 7: Getting Started: Roots of a Function ............
Page 6 Table of Contents (continued) Chapter 10: Getting Started: Systems of Linear Equations 10-2 ........Matrices Defining a Matrix 10-3 ....................Viewing and Editing Matrix Elements 10-4 ............Using Matrices with Expressions 10-7 ..............Displaying and Copying Matrices 10-8 ..............Using Math Functions with Matrices 10-9 ............
Page 7 Calculating Interest Conversion 14-12 ..............Finding Days between Dates/Defining Payment Method 14-13 ....... Using the Variables 14-14 ................... Chapter 15: Browsing the TI-82 STATS 15-2 CATALOG ..........Entering and Using Strings 15-3 CATALOG ................Strings, Storing Strings to String Variables 15-4 ..............
Page 8 Receiving Items 19-5 ....................... Transmitting Items 19-6 ....................Transmitting Lists to a TI-82 19-8 ................Transmitting from a TI-82 to a TI-82 STATS 19-9 ........Backing Up Memory 19-10 .................... Appendix A: Table of Functions and Instructions ............Tables and...
Page 9 Setting the Viewing Window: Box with Lid ......... Displaying and Tracing the Graph: Box with Lid ......Zooming In on the Graph: Box with Lid ..........Finding the Calculated Maximum: Box with Lid ......Other TI-82 STATS Features ................Getting Started 1...
Page 10: Ti-82 Stats Keyboard
TI-82 STATS Keyboard Generally, the keyboard is divided into these zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys. Graphing keys access the interactive graphing features. Keyboard Zones Editing keys allow you to edit expressions and values.
Page 11 The keys on the TI-82 STATS are color-coded to help you Using the easily locate the key you need. Color.Coded Keyboard The gray keys are the number keys. The blue keys along the right side of the keyboard are the common math functions. The blue keys across the top set up and display graphs.
Page 12: Ti-82 Stats Menus
TI-82 STATS Menus Displaying a Menu While using your TI-82 STATS, you often will need to access items from its menus. When you press a key that displays a menu, that menu temporarily replaces the screen where you are working. For example, when you press , menu is displayed as a full screen.
Page 13: First Steps
Before starting the sample problems in this chapter, follow the steps on this page to reset the TI-82 STATS to its factory settings and clear all memory. This ensures that the keystrokes in this chapter will produce the illustrated results.
Page 14: Entering A Calculation: The Quadratic Formula
Entering a Calculation: The Quadratic Formula Use the quadratic formula to solve the quadratic equations 3X + 5X + 2 = 0 and 2X N X + 3 = 0. Begin with the equation 3X + 5X + 2 = 0. ¿...
Page 15: Converting To A Fraction: The Quadratic Formula
Converting to a Fraction: The Quadratic Formula You can show the solution as a fraction. 1. Press  to display the menu. MATH 2. Press to select from the menu. 1:4Frac MATH When you press is displayed on Ans4Frac the home screen. is a variable that contains the last calculated answer.
Page 16: Displaying Complex Results: The Quadratic Formula
Now solve the equation 2X N X + 3 = 0. When you set i complex number mode, the TI-82 STATS displays complex results. 1. Press z † † † † † † (6 times), and then press ~ to position the cursor over Press Í...
Page 17: Defining A Function: Box With Lid
Defining a Function: Box with Lid Take a 20 cm. × 25 cm. sheet of paper and cut X × X squares from two corners. Cut X × 12.5 cm. rectangles from the other two corners as shown in the diagram below. Fold the paper into a box with a lid.
Page 18: Defining A Table Of Values: Box With Lid
Defining a Table of Values: Box with Lid The table feature of the TI-82 STATS displays numeric information about a function. You can use a table of values from the function defined on page 9 to estimate an answer to the problem.
Page 19: Zooming In On The Table: Box With Lid
Zooming In on the Table: Box with Lid You can adjust the way a table is displayed to get more information about a defined function. With smaller values for , you can zoom in on the table. @Tbl Í to set .
Page 20: Setting The Viewing Window: Box With Lid
Setting the Viewing Window: Box with Lid You also can use the graphing features of the TI-82 STATS to find the maximum value of a previously defined function. When the graph is activated, the viewing window defines the displayed portion of the coordinate plane. The values of the window variables determine the size of the viewing window.
Page 21: Displaying And Tracing The Graph: Box With Lid
Displaying and Tracing the Graph: Box with Lid Now that you have defined the function to be graphed and the window in which to graph it, you can display and explore the graph. You can trace along a function using feature.
Page 22 Displaying and Tracing the Graph: Box with Lid (cont.) 4. Press r. The trace cursor is displayed on function. The function that you are tracing is displayed in the top-left corner. 5. Press | and ~ to trace along , one dot at a time, evaluating at each...
Page 23: Zooming In On The Graph: Box With Lid
1. Press q to display the menu. ZOOM This menu is a typical TI-82 STATS menu. To select an item, you can either press the number or letter next to the item, or you can press † until the item number or letter is highlighted, and then press Í.
Page 24: Finding The Calculated Maximum: Box With Lid
Finding the Calculated Maximum: Box with Lid You can use a menu operation to calculate a local maximum of a CALCULATE function. 1. Press y [ ] (above r) to display the CALC menu. Press to select CALCULATE 4:maximum The graph is displayed again with a prompt.
Page 25: Other Ti-82 Stats Features
Other TI-82 STATS Features Getting Started has introduced you to basic TI-82 STATS operation. This guidebook describes in detail the features you used in Getting Started. It also covers the other features and capabilities of the TI-82 STATS. You can store, graph, and analyze up to 10 functions (Chapter...
Page 26 TI Connect™ software and a TI Connectivity cable. The or Macintoshë software is included on the CD in the TI-82 STATS package. When you connect to the TI Connect™ software, the TI-82 STATS calculator will be identified by TI Connect™ as a TI-83 calculator.
Page 27 Operating the TI-82 STATS Contents Turning On and Turning Off the TI-82 STATS ......... Setting the Display Contrast ................The Display ........................ Entering Expressions and Instructions ............TI-82 STATS Edit Keys ..................Setting Modes ......................Using TI-82 STATS Variable Names ............
Page 28: Turning On And Turning Off The Ti-82 Stats
If Automatic Power Down™ (APDé) had previously turned off the calculator, the TI-82 STATS will return exactly as you left it, including the display, cursor, and any error. To prolong the life of the batteries, APD turns off the TI-82 STATS automatically after about five minutes without any activity.
Page 29: Setting The Display Contrast
(darkest) in the top-right corner indicates the current level. You may not be able to see the number if contrast is too light or too dark. Note: The TI-82 STATS has 40 contrast settings, so each number through represents four settings.
Page 30: The Display
Displays display a horizontally or vertically split screen to show graphs and text simultaneously. The home screen is the primary screen of the TI-82 STATS. On Home Screen this screen, enter instructions to execute and expressions to evaluate. The answers are displayed on the same screen.
Page 31 If you press ƒ during an insertion, the cursor becomes an ) If you press y during an insertion, the underlined underline cursor becomes an underlined # ( # ). Graphs and editors sometimes display additional cursors, which are described in other chapters. Operating the TI-82 STATS 1-5...
Page 32: Entering Expressions And Instructions
What Is an their arguments, or a combination of these elements. An Expression? expression evaluates to a single answer. On the TI-82 STATS, you enter an expression in the same order as you would write it on paper. For example, pR is an expression.
Page 33 ‡( the functions in the example on page 1.6. In general, the first letter of each function is lowercase on the TI-82 STATS. Most functions take at least one argument, as indicated by an open parenthesis ( ) following the name. For example,...
Page 34: Ti-82 Stats Edit Keys
] Changes the cursor to Ø; sets alpha-lock; subsequent keystrokes (on an LOCK alpha key) paste alpha characters; to cancel alpha-lock, press ƒ; name prompts set alpha-lock automatically. „ Pastes an mode, a mode, a mode, or an Func mode with one keystroke. 1-8 Operating the TI-82 STATS...
Page 35: Setting Modes
Checking Mode interprets numbers and graphs. Mode settings are retained by the Settings Constant Memory feature when the TI-82 STATS is turned off. All numbers, including elements of matrices and lists, are displayed according to the current mode settings. To display the mode settings, press z. The current settings are highlighted.
Page 36 Note: If you select notation, but the answer cannot display in 10 digits (or the absolute value is less than .001), the TI-82 STATS expresses the answer in scientific notation. (floating) decimal mode displays up to 10 digits, plus the...
Page 37 Angle modes control how the TI-82 STATS interprets angle Radian, Degree values in trigonometric functions and polar/rectangular conversions. mode interprets angle values as radians. Answers Radian display in radians. mode interprets angle values as degrees. Answers Degree display in degrees.
Page 38 Note: Regardless of which graphing mode is selected, the TI-82 STATS will sequentially graph all stat plots before it graphs any functions. mode does not display complex results unless complex...
Page 39: Using Ti-82 Stats Variable Names
Using TI-82 STATS Variable Names On the TI-82 STATS you can enter and use several types of Variables and data, including real and complex numbers, matrices, lists, Defined Items functions, stat plots, graph databases, graph pictures, and strings. The TI-82 STATS uses assigned names for variables and other items saved in memory.
Page 40: Storing Variable Values
4. Press Í. If you entered an expression, it is evaluated. The value is stored to the variable. To display the value of a variable, enter the name on a blank Displaying a line on the home screen, and then press Í. Variable Value 1-14 Operating the TI-82 STATS...
Page 41: Recalling Variable Values
3. Press Í. The variable contents are inserted where the cursor was located before you began these steps. Note: You can edit the characters pasted to the expression without affecting the value in memory. Operating the TI-82 STATS 1-15...
Page 42: Entry (Last Entry) Storage Area
Í, you can recall the previous entry even if you have begun to enter the next expression. Ã Í ENTRY The TI-82 STATS retains as many previous entries as possible Accessing a , up to a capacity of 128 bytes. To scroll those entries, Previous Entry ENTRY press y [ ] repeatedly.
Page 43 ] ƒ ¡ Í ENTRY ] Ë Í Continue until the answer is as accurate as you want. (Chapter 18) clears all data that the TI-82 STATS Clearing ENTRY Clear Entries is holding in the storage area. ENTRY Operating the TI-82 STATS 1-17...
Page 44: Ans (Last Answer) Storage Area
Ans (Last Answer) Storage Area When an expression is evaluated successfully from the home Using Ans in an screen or from a program, the TI-82 STATS stores the answer to Expression a storage area called (last answer). may be a real or complex number, a list, a matrix, or a string.
Page 45: Ti-82 Stats Menus
TI-82 STATS Menus You can access most TI-82 STATS operations using menus. Using a When you press a key or key combination to display a menu, TI-82 STATS one or more menu names appear on the top line of the screen.
Page 46 Press † or } to move the cursor to the item you want, and then press Í. After you select an item from a menu, the TI-82 STATS typically displays the previous screen. LIST NAMES...
Page 47: Vars And Vars Y.vars Menus
, or from the 1:Window 2:Zoom 5:Statistics menu, you can press ~ or | to display other VARS secondary menus. 4. Select a variable name from the menu. It is pasted to the cursor location. Operating the TI-82 STATS 1-21...
Page 48: Equation Operating System (Eosé)
Order of which functions in expressions are entered and evaluated on the Evaluation TI-82 STATS. EOS lets you enter numbers and functions in a simple, straightforward sequence. EOS evaluates the functions in an expression in this order: Single-argument functions that precede the argument,...
Page 49 To enter a negative number, use the negation key. Press Ì and Negation then enter the number. On the TI-82 STATS, negation is in the third level in the EOS hierarchy. Functions in the first level, such as squaring, are evaluated before negation.
Page 50: Error Conditions
Evaluating an expression Executing an instruction Plotting a graph Storing a value When the TI-82 STATS detects an error, it returns an error message as a menu title, such as ERR:SYNTAX . Appendix B describes each error type and ERR:DOMAIN possible reasons for the error.
Page 51 Math, Angle, and Test Operations Contents Getting Started: Coin Flip ................. Keyboard Math Operations ................Operations MATH ....................Using the Equation Solver ................(Number) Operations MATH NUM .............. Entering and Using Complex Numbers ............ (Complex) Operations MATH CPX ............(Probability) Operations MATH PRB ............
Page 52: Getting Started: Coin Flip
Getting Started: Coin Flip Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10 coin flips result in heads. You want to perform this simulation 40 times.
Page 53: Keyboard Math Operations
Keyboard Math Operations Math operations that are valid for lists return a list calculated Using Lists with element by element. If you use two lists in the same expression, Math Operations they must be the same length. (addition, Ã), (subtraction, ¹), ä...
Page 54 ( ), which is displayed when you press ¹. (Pi, y [ ]) is stored as a constant in the TI-82 STATS. In p (Pi) calculations, the TI-82 STATS uses 3.1415926535898 for 2.4 Math, Angle, and Test Operations...
Page 55: Math Operations
MATH Operations menu, press . To display the MATH Menu MATH NUM CPX PRB Displays the answer as a fraction. 1: 4Frac Displays the answer as a decimal. 2: 4Dec Calculates the cube. Calculates the cube root. ‡( Calculates the x root.
Page 56 MATH Operations (continued) (cube) returns the cube of value. You can use with real or (Cube), complex numbers, expressions, lists, and square matrices. ‡( (Cube Root) value (cube root) returns the cube root of value. You can use ‡( ‡( with real or complex numbers, expressions, and lists.
Page 57 As H becomes smaller, the approximation usually becomes more accurate. You can use once in expression. Because of the method nDeriv( used to calculate , the TI-82 STATS can return a false nDeriv( derivative value at a nondifferentiable point. (function integral) returns the numerical integral (Gauss- fnInt( fnInt(...
Page 58: Using The Equation Solver
Using the Equation Solver displays the equation solver, in which you can solve for Solver Solver any variable in an equation. The equation is assumed to be equal to zero. is valid only for real numbers. Solver When you select , one of two screens is displayed.
Page 59 3. Press Í or †. The interactive solver editor is displayed. Entering an Expression in the Equation Solver (continued) The equation stored in is set equal to zero and displayed on the top line. Variables in the equation are listed in the order in which they appear in the equation.
Page 60 3. Enter an initial guess for the variable for which you are solving. This is optional, but it may help find the solution more quickly. Also, for equations with multiple roots, the TI-82 STATS will attempt to display the solution that is closest to your guess. (upper + lower) The default guess is calculated as 2.10 Math, Angle, and Test Operations...
Page 61 . lower and upper are the bounds Solving for a bound={ between which the TI-82 STATS searches for a solution. This is Variable in the optional, but it may help find the solution more quickly. The Equation Solver default is (continued) å...
Page 62 Move the cursor to the variable for which you now want to solve and press ƒ [ SOLVE The TI-82 STATS solves equations through an iterative process. Controlling the To control that process, enter bounds that are relatively close to Solution for the solution and enter an initial guess within those bounds.
Page 63: Math Num (Number) Operations
MATH NUM (Number) Operations menu, press  ~. To display the MATH NUM Menu MATH NUM MATH NU CPX PRB Absolute value 1: abs( Round 2: round( Integer part 3: iPart( Fractional part 4: fPart( Greatest integer 5: int( Minimum value 6: min( Maximum value 7: max(...
Page 64 MATH NUM (Number) Operations (continued) (integer part) returns the integer part or parts of real or iPart(, iPart( complex numbers, expressions, lists, and matrices. fPart( value iPart( (fractional part) returns the fractional part or parts of real or fPart( complex numbers, expressions, lists, and matrices. value fPart( (greatest integer) returns the largest integer ...
Page 65 (minimum value) returns the smaller of valueA and valueB min(, min( or the smallest element in list. If listA and listB are compared, max( returns a list of the smaller of each pair of elements. If list min( and value are compared, compares each element in list min( with value.
Page 66: Entering And Using Complex Numbers
(rectangular-complex mode) i (polar-complex mode) re^q On the TI-82 STATS, complex numbers can be stored to variables. Also, complex numbers are valid list elements. mode, complex-number results return an error, unless Real you entered a complex number as input.
Page 67 Complex numbers in results, including list elements, are Interpreting displayed in either rectangular or polar form, as specified by the Complex Results mode setting or by a display conversion instruction (page 2.19). In the example below, i and modes are set. re^q Radian Rectangular-complex mode recognizes and displays a complex...
Page 68: Math Cpx (Complex) Operations
MATH CPX (Complex) Operations menu, press  ~ ~. To display the MATH CPX Menu MATH CPX MATH NU CPX PRB Returns the complex conjugate. 1: conj( Returns the real part. 2: real( Returns the imaginary part. 3: imag( Returns the polar angle. 4: angle( Returns the magnitude (modulus).
Page 69 returns the polar angle of a complex number or list of angle( angle( complex numbers, calculated as tan (b/a), where b is the imaginary part and a is the real part. The calculation is adjusted by +p in the second quadrant or Np in the third quadrant. returns tan (b/a).
Page 70: Math Prb (Probability) Operations
For example, generates a random number > 0 and < 5. With each execution, the TI-82 STATS generates the same rand random-number sequence for a given seed value. The TI-82 STATS factory-set seed value for . To generate a...
Page 71 (number of permutations) returns the number of nPr, permutations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists. items number (number of combinations) returns the number of combinations of items taken number at a time. items and number must be nonnegative integers.
Page 72 MATH PRB (Probability) Operations (continued) (random integer) generates and displays a random randInt( randInt( integer within a range specified by lower and upper integer bounds. To generate a list of random numbers, specify an integer >1 for numtrials (number of trials); if not specified, the default is 1.
Page 73: Angle Operations
For example, enter for 30 degrees, 1 minute, 23 seconds. If the angle mode is not set to , you must use so that the Degree ¡ TI-82 STATS can interpret the argument as degrees, minutes, and seconds. mode mode Degree Radian (degree) designates an angle or list of angles as degrees, ¡...
Page 74 ANGLE Operations (continued) (radians) designates an angle or list of angles as radians, (Radians) regardless of the current angle mode setting. In mode, Degree you can use to convert radians to degrees. value mode Degree (degree/minute/second) displays answer in DMS format 8DMS 8DMS (page 2.23).
Page 75: Test (Relational) Operations
Relational operators are evaluated after mathematical functions Using Tests according to EOS rules (Chapter 1). The expression returns . The TI-82 STATS 2+2=2+3 performs the addition first because of EOS rules, and then it compares 4 to 5. The expression returns .
Page 76: Test Logic (Boolean) Operations
TEST LOGIC (Boolean) Operations menu, press y ã ä ~. To display the TEST LOGIC TEST LOGIC TEST Menu This operator... Returns a 1 (true) if... TEST LOGIC Both values are nonzero (true). 1: and At least one value is nonzero (true). 2: or Only one value is zero (false).
Page 77 Function Graphing Contents Getting Started: Graphing a Circle .............. Defining Graphs ...................... Setting the Graph Modes ................... Defining Functions ....................Selecting and Deselecting Functions ............Setting Graph Styles for Functions .............. Setting the Viewing Window Variables ........... Setting the Graph Format ..................
Page 78: Getting Started: Graphing A Circle
The expression Y=L‡(100NX ) defines the bottom half of the circle. On the TI-82 STATS, you can define one function in terms of another. , press Ì to enter the negation To define sign.
Page 79: Defining Graphs
Defining Graphs Chapter 3 specifically describes function graphing, but the steps TI-82 STATS— shown here are similar for each TI-82 STATS graphing mode. Graphing Mode Chapters 4, 5, and 6 describe aspects that are unique to Similarities parametric graphing, polar graphing, and sequence graphing.
Page 80: Setting The Graph Modes
Changing the Func mode before you enter values for the window variables and Graphing Mode before you enter the functions. The TI-82 STATS has four graphing modes. (function graphing) Func (parametric graphing; Chapter 4) (polar graphing; Chapter 5) (sequence graphing; Chapter 6) Other mode settings affect graphing results.
Page 81: Defining Functions
Defining Functions editor, press o. You can store up to 10 To display the Displaying functions to the function variables through , and . You Functions in the can graph one or more defined functions at once. In this Y= Editor example, functions are defined and selected.
Page 82 5. Press Í to complete the instruction. "! ! ! ! Y expression " When the instruction is executed, the TI-82 STATS stores the expression to the designated variable n, selects the function, and displays the message Done...
Page 83: Selecting And Deselecting Functions
You can select and deselect (turn on and turn off) a function in Selecting and editor. A function is selected when the sign is Deselecting a highlighted. The TI-82 STATS graphs only the selected Function functions. You can select any or all functions through , and...
Page 84 Selecting and Deselecting Functions (continued) To select or deselect a function from the home screen or a Selecting and program, begin on a blank line and follow these steps. Deselecting Functions from 1. Press  ~ to display the menu. VARS Y.VARS the Home Screen or a Program...
Page 85: Setting Graph Styles For Functions
Setting Graph Styles for Functions This table describes the graph styles available for function Graph Style graphing. Use the styles to visually differentiate functions to be Icons in the Y= graphed together. For example, you can set as a solid line, Editor as a dotted line, and as a thick line.
Page 86 Setting Graph Styles for Functions (continued) When you select é or ê for two or more functions, the Shading Above TI-82 STATS rotates through four shading patterns. and Below Vertical lines shade the first function with a é or ê graph style.
Page 87: Setting The Viewing Window Variables
Enter a new value, which clears the original value. Move the cursor to a specific digit, and then edit it. 3. Press Í, †, or }. If you entered an expression, the TI-82 STATS evaluates it. The new value is stored. Xmin Xmax...
Page 88 The name of the variable is pasted to the current cursor location. 6. Press Í to complete the instruction. When the instruction is executed, the TI-82 STATS stores the value to the window variable and displays the value. The variables...
Page 89: Setting The Graph Format
Setting the Graph Format To display the format settings, press y [ ]. The default Displaying the FORMAT settings are highlighted below. Format Settings Sets cursor coordinates. RectGC PolarGC Sets coordinates display on or off. CoordOn CoordOff Sets grid off or on. GridOff GridOn Sets axes on or off.
Page 90 Setting the Graph Format (continued) (coordinates on) displays the cursor coordinates at the CoordOn, CoordOn bottom of the graph. If format is selected, the function CoordOff ExprOff number is displayed in the top-right corner. (coordinates off) does not display the function number CoordOff or coordinates.
Page 91: Displaying Graphs
Press Í to pause; then press Í to resume. Press É to stop; then press s to redraw. Smart Graph is a TI-82 STATS feature that redisplays the last Smart Graph graph immediately when you press s, but only if all graphing factors that would cause replotting have remained the same since the graph was last displayed.
Page 92 Displaying Graphs (continued) On the TI-82 STATS, you can graph one or more new functions Overlaying without replotting existing functions. For example, store Functions on a sin(X) editor and press s. Then store in the Graph cos(X) and press s again. The function is graphed on top of the original function.
Page 93: Exploring Graphs With The Free-Moving Cursor
Exploring Graphs with the Free-Moving Cursor When a graph is displayed, press |, ~, }, or † to move the Free-Moving cursor around the graph. When you first display the graph, no Cursor cursor is visible. When you press |, ~, }, or †, the cursor moves from the center of the viewing window.
Page 94: Exploring Graphs With Trace
Exploring Graphs with TRACE to move the cursor from one plotted point to the Beginning a TRACE next along a function. To begin a trace, press r. If the Trace graph is not displayed already, press r to display it. The trace cursor is on the first selected function in the editor, at the middle...
Page 95 To move the trace cursor to any valid value on the current Moving the Trace function, enter the value. When you enter the first digit, an Cursor to Any prompt and the number you entered are displayed in the bottom- Valid X Value left corner of the screen.
Page 96: Exploring Graphs With The Zoom Instructions
Exploring Graphs with the ZOOM Instructions menu, press q. You can adjust the To display the ZOOM Menu ZOOM viewing window of the graph quickly in several ways. All instructions are accessible from programs. ZOOM MEMORY Draws a box to define the viewing window. 1: ZBox Magnifies the graph around the cursor.
Page 97 ZOOM displayed. 3. Move the zoom cursor to the point that is to be the center of the new viewing window. 4. Press Í. The TI-82 STATS adjusts the viewing window ; updates the window variables; and XFact YFact replots the selected functions, centered on the cursor location.
Page 98 Exploring Graphs with the ZOOM Instructions (cont.) replots the functions immediately. It updates the ZStandard ZStandard window variables to the standard values shown below. Xmin=L10 Ymin=L10 Xres=1 Xmax=10 Ymax=10 Xscl=1 Yscl=1 ZTrig replots the functions immediately. It updates the window ZTrig variables to preset values that are appropriate for plotting trig functions.
Page 99: Using Zoom Memory
Using ZOOM MEMORY menu, press q ~. To display the ZOOM MEMORY ZOOM MEMORY Menu ZOOMMEMOR Uses the previous viewing window. 1: ZPrevious Stores the user-defined window. 2: ZoomSto Recalls the user-defined window. 3: ZoomRcl Changes factors. Zoom In Zoom Out 4: SetFactors...
Page 100 Using ZOOM MEMORY (continued) The zoom factors, , are positive numbers (not ZOOM FACTORS XFact YFact necessarily integers) greater than or equal to 1. They define the magnification or reduction factor used to Zoom In Zoom Out around a point. To display the screen, where you can review Checking XFact...
Page 101: Using The Calc (Calculate) Operations
Using the CALC (Calculate) Operations menu, press y ã To display the ä. Use the CALCULATE CALCULATE CALC items on this menu to analyze the current graph functions. Menu CALCULAT Calculates a function value for a given 1: value Finds a zero (x-intercept) of a function. 2: zero Finds a minimum of a function.
Page 102 Using the CALC (Calculate) Operations (continued) finds a zero (x-intercept or root) of a function using zero zero solve( Functions can have more than one x-intercept value; finds zero the zero closest to your guess. The time spends to find the correct zero value depends on zero the accuracy of the values you specify for the left and right bounds and the accuracy of your guess.
Page 103 find a minimum or maximum of a minimum, minimum maximum function within a specified interval to a tolerance of 1âL5. maximum To find a minimum or maximum, follow these steps. 1. Select from the 3:minimum 4:maximum CALCULATE menu. The current graph is displayed. 2.
Page 104 Using the CALC (Calculate) Operations (continued) (numerical derivative) finds the numerical derivative dy/dx dy/dx (slope) of a function at a point, with H=1âL3. To find a function’s slope at a point, follow these steps. 1. Select from the menu. The current 6:dy/dx CALCULATE graph is displayed.
Page 105 Parametric Graphing Contents Getting Started: Path of a Ball ................ Defining and Displaying Parametric Graphs ........Exploring Parametric Graphs ................Parametric Graphing 4-1...
Page 106: Getting Started: Path Of A Ball
Getting Started: Path of a Ball Getting Started is a fast-paced introduction. Read the chapter for details. Graph the parametric equation that describes the path of a ball hit at an initial speed of 30 meters per second, at an initial angle of 25 degrees with the horizontal from ground level.
Page 107 The horizontal component vector is defined by 6. Press  ~ Í to , and then press Í to define define . Press 7. Press | | } Í to change the graph style to è for . Press } Í Í...
Page 108: Defining And Displaying Parametric Graphs
Defining and Displaying Parametric Graphs The steps for defining a parametric graph are similar to the steps TI-82 STATS for defining a function graph. Chapter 4 assumes that you are Graphing Mode familiar with Chapter 3: Function Graphing. Chapter 4 details...
Page 109 Press ƒ ã ä. Two components, , define a single parametric equation. You must define both of them. The TI-82 STATS graphs only the selected parametric Selecting and equations. In the editor, a parametric equation is selected Deselecting when the...
Page 110 Format FORMAT other graphing modes share these format settings; graphing mode has an additional axes format setting. When you press s, the TI-82 STATS plots the selected Displaying a parametric equations. It evaluates the components for Graph each value of...
Page 111: Exploring Parametric Graphs
Exploring Parametric Graphs The free-moving cursor in graphing works the same as in Free-Moving graphing. Cursor Func format, moving the cursor updates the values of RectGC ; if format is selected, are displayed. CoordOn format, , and are updated; if PolarGC CoordOn format is selected,...
Page 112 Exploring Parametric Graphs (continued) To move the trace cursor to any valid value on the current Moving the Trace function, enter the number. When you enter the first digit, a Cursor to Any prompt and the number you entered are displayed in the bottom- Valid T Value left corner of the screen.
Page 113 Polar Graphing Contents Getting Started: Polar Rose ................Defining and Displaying Polar Graphs ............. Exploring Polar Graphs ..................Polar Graphing 5–1...
Page 114: Getting Started: Polar Rose
Getting Started: Polar Rose Getting Started is a fast-paced introduction. Read the chapter for details. The polar equation R=Asin(Bq) graphs a rose. Graph the rose for A=8 and B=2.5, and then explore the appearance of the rose for other values of A and B. 1.
Page 115: Defining And Displaying Polar Graphs
Defining and Displaying Polar Graphs The steps for defining a polar graph are similar to the steps for TI-82 STATS defining a function graph. Chapter 5 assumes that you are Graphing Mode familiar with Chapter 3: Function Graphing. Chapter 5 details Similarities aspects of polar graphing that differ from function graphing.
Page 116 Equations enter the polar variable in either of two ways. Press „. Press ƒ ãqä. The TI-82 STATS graphs only the selected polar equations. In Selecting and editor, a polar equation is selected when the sign is Deselecting Polar highlighted. You may select any or all of the equations.
Page 117 ]. Chapter 3 describes the format settings in detail. The Format FORMAT other graphing modes share these format settings. When you press s, the TI-82 STATS plots the selected Displaying a polar equations. It evaluates for each value of (from...
Page 118: Exploring Polar Graphs
Exploring Polar Graphs The free-moving cursor in graphing works the same as in Free-Moving graphing. In format, moving the cursor updates Cursor Func RectGC the values of ; if format is selected, CoordOn are displayed. In format, , and are updated; if PolarGC format is selected, are displayed.
Page 119 Selecting Axes Combinations ................. Exploring Sequence Graphs ................Graphing Web Plots ....................Using Web Plots to Illustrate Convergence ........... Graphing Phase Plots ................... Comparing TI-82 STATS and TI.82 Sequence Variables ... Keystroke Differences Between TI-82 STATS and TI-82 ..Sequence Graphing 6–1...
Page 120: Getting Started: Forest And Trees
Getting Started: Forest and Trees Getting Started is a fast-paced introduction. Read the chapter for details. A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of the trees will be harvested and 1,000 new trees will be planted. Will the forest eventually disappear? Will the forest size stabilize? If so, in how many years and with how many trees? 1.
Page 121: Sequence
Sequence graphs automatically plot in mode, regardless Simul of the current plotting-order mode setting. The TI-82 STATS has three sequence functions that you can TI-82 STATS . They are above the ¬, −, enter from the keyboard: , and Sequence and ®...
Page 122 í (dot), which shows discrete values. Dot, ç (line), and è (thick) styles are available for sequence graphing. Graph styles are ignored in format. The TI-82 STATS graphs only the selected sequence functions. Selecting and In the editor, a sequence function is selected when the...
Page 123 To define or edit a sequence function, follow the steps in Defining and Chapter 3 for defining a function. The independent variable in a Editing a sequence is Sequence Function graphing mode, you can enter the sequence variable in either of two ways. Press „.
Page 124 Using an initial value , the sequence above returns u(nMin) = 1 , . . . Tip: On the TI-82 STATS, you must type each character of the terms. , press y [ ] £ „ ¹ À ¤. u(nN1)
Page 125 To display the window variables, press p. These Setting Window variables define the viewing window. The values below are Variables defaults for graphing in both angle Radian Degree modes. Smallest value to evaluate nMin=1 Largest value to evaluate nMax=10 First term number to be plotted PlotStart=1 Incremental value (for graphing only)
Page 126: Selecting Axes Combinations
See page 6.13 for more information on phase plots ( , and axes settings). To plot the selected sequence functions, press s. As a Displaying a graph is plotted, the TI-82 STATS updates , and Sequence Graph Smart Graph applies to sequence graphs (Chapter 3). 6–8 Sequence Graphing...
Page 127: Exploring Sequence Graphs
Exploring Sequence Graphs The free-moving cursor in graphing works the same as in Free-Moving graphing. In format, moving the cursor updates Cursor Func RectGC the values of ; if format is selected, CoordOn are displayed. In format, , and are updated; if PolarGC format is selected, are displayed.
Page 128 Exploring Sequence Graphs (continued) operations in graphing work the same as in ZOOM ZOOM Func graphing. Only the , and ) and Xmin Xmax Xscl Ymin , and ) window variables are affected. Ymax Yscl , and are only affected when PlotStart PlotStep nMin...
Page 129: Graphing Web Plots
It cannot reference directly. It cannot reference any defined sequence except itself. format, press s to display the graph screen. The Displaying the TI-82 STATS: Graph Screen Draws a reference line in format. AxesOn Plots the selected sequences with...
Page 130: Using Web Plots To Illustrate Convergence
Using Web Plots to Illustrate Convergence 1. Press o in mode to display the sequence editor. Make Example: sure the graph style is set to í (dot), and then define Convergence nMin u(n) as shown below. u(nMin) 2. Press y [ ] Í...
Page 131: Graphing Phase Plots
Graphing Phase Plots The phase-plot axes settings , and show relationships Graphing with uv, between two sequences. To select a phase-plot axes setting, vw, and uw press y [ ], press ~ until the cursor is on , or FORMAT , and then press Í.
Page 132 Graphing Phase Plots (continued) 2. Press y [ ] Í to select Example: axes format. Time FORMAT Predator-Prey 3. Press p and set the variables as shown below. Model nMin=0 Xmin=0 Ymin=0 (continued) nMax=400 Xmax=400 Ymax=300 PlotStart=1 Xscl=100 Yscl=100 PlotStep=1 4.
Page 133: Comparing Ti-82 Stats And Ti.82 Sequence Variables
Comparing TI-82 STATS and TI-82 Sequence Variables Refer to the table if you are familiar with the TI-82. It shows Sequences and TI-82 STATS sequences and sequence window variables, as Window well as their TI-82 counterparts. Variables TI-82 STATS TI.82...
Page 134: Keystroke Differences Between Ti-82 Stats And
Keystroke Differences Between TI-82 STATS and TI-82 Refer to the table if you are familiar with the TI-82. It compares Sequence TI-82 STATS sequence-name syntax and variable syntax with Keystroke TI.82 sequence-name syntax and variable syntax. Changes TI-82 STATS / On TI-82 STATS, On TI.82, press:...
Page 135 Tables Contents Getting Started: Roots of a Function ............Setting Up the Table ..................... Defining the Dependent Variables ............... Displaying the Table ..................... Tables 7–1...
Page 136: Getting Started: Roots Of A Function
Getting Started: Roots of a Function Getting Started is a fast-paced introduction. Read the chapter for details. Evaluate the function Y = X N 2X at each integer between L10 and 10. How many sign changes occur, and at what values? 1.
Page 137: Setting Up The Table
Setting Up the Table screen, press y [ To display the TABLE SETUP TABLE SETUP TBLSET Screen (table start) defines the initial value for the independent TblStart, @Tbl TblStart variable. applies only when the independent variable is TblStart generated automatically (when is selected).
Page 138: Defining The Dependent Variables
Defining the Dependent Variables In the editor, enter the functions that define the dependent Defining variables. Only functions that are selected in the editor are Dependent displayed in the table. The current graphing mode is used. In Variables from mode, you must define both components of each parametric the Y= Editor equation (Chapter 4).
Page 139: Displaying The Table
Displaying the Table To display the table, press y [ The Table TABLE Current cell Independent- Dependent- variable values variable values in in the first the second and column third columns Current cell’s full value Note: The table abbreviates the values, if necessary. The current graphing mode determines which independent and Independent and dependent variables are displayed in the table (Chapter 1).
Page 140 Displaying the Table (continued) is selected, you can press } and † in the Scrolling Indpnt: Auto independent-variable column to display more values. As you Independent- scroll the column, the corresponding dependent-variable values Variable Values also are displayed. All dependent-variable values may not be displayed if is selected.
Page 141 Draw Instructions Contents Getting Started: Drawing a Tangent Line ..........Using the Menu DRAW ..................Clearing Drawings ....................Drawing Line Segments ..................Drawing Horizontal and Vertical Lines ........... Drawing Tangent Lines ..................Drawing Functions and Inverses ..............Shading Areas on a Graph ................
Page 142: Getting Started: Drawing A Tangent Line
Getting Started: Drawing a Tangent Line Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to find the equation of the tangent line at X = ‡2/2 for the function Y = sinX. Before you begin, select mode Radian Func...
Page 143: Using The Draw Menu
To display the ]. The DRAW Menu DRAW DRAW TI-82 STATS interpretation of these instructions depends on whether you accessed the menu from the home screen or the program editor or directly from a graph. POINTS STO Clears all drawn elements.
Page 144: Clearing Drawings
Clearing Drawings All points, lines, and shading drawn on a graph with Clearing DRAW instructions are temporary. Drawings When a Graph Is To clear drawings from the currently displayed graph, select Displayed from the menu. The current graph is replotted 1:ClrDraw DRAW and displayed with no drawn elements.
Page 145: Drawing Line Segments
Drawing Line Segments To draw a line segment when a graph is displayed, follow these Drawing a Line steps. Segment Directly on a Graph 1. Select from the menu. 2:Line( DRAW 2. Place the cursor on the point where you want the line segment to begin, and then press Í.
Page 146: Drawing Horizontal And Vertical Lines
Drawing Horizontal and Vertical Lines To draw a horizontal or vertical line when a graph is displayed, Drawing a Line follow these steps. Directly on a Graph 1. Select from the menu. A 3:Horizontal 4:Vertical DRAW line is displayed that moves as you move the cursor. 2.
Page 147 (vertical line) draws a vertical line at =x. x can be an Vertical expression but not a list. Vertical To instruct the TI-82 STATS to draw more than one horizontal or vertical line, separate each instruction with a colon ( Instructions 8–7 DRAW...
Page 148: Drawing Tangent Lines
Drawing Tangent Lines To draw a tangent line when a graph is displayed, follow these Drawing steps. a Tangent Line Directly 1. Select from the menu. 5:Tangent( DRAW on a Graph 2. Press † and } to move the cursor to the function for which you want to draw the tangent line.
Page 149: Drawing Functions And Inverses
(draw function) draws expression as a function in terms Drawing a DrawF on the current graph. When you select from the Function 6:DrawF menu, the TI-82 STATS returns to the home screen or DRAW the program editor. is not interactive. DrawF expression DrawF Note: You cannot use a list in expression to draw a family of curves.
Page 150: Shading Areas On A Graph
Shading Areas on a Graph To shade an area on a graph, select from the Shading a Graph 7:Shade( DRAW menu. The instruction is pasted to the home screen or to the program editor. draws lowerfunc and upperfunc in terms of on the Shade( current graph and shades the area that is specifically above...
Page 151: Drawing Circles
Drawing Circles To draw a circle directly on a displayed graph using the cursor, Drawing a Circle follow these steps. Directly on a Graph 1. Select from the menu. 9:Circle( DRAW 2. Place the cursor at the center of the circle you want to draw. Press Í.
Page 152: Placing Text On A Graph
3. Enter the characters. Press ƒ or y [ ] to enter A.LOCK letters and q. You may enter TI-82 STATS functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies.
Page 153: Using Pen To Draw On A Graph
Using Pen to Draw on a Graph draws directly on a graph only. You cannot execute Using Pen to from the home screen or a program. Draw on a Graph To draw on a displayed graph, follow these steps. 1. Select from the menu.
Page 154: Drawing Points On A Graph
] ~. The To display the DRAW POINTS DRAW POINTS DRAW TI-82 STATS interpretation of these instructions depends on Menu whether you accessed this menu from the home screen or the program editor or directly from a graph. DRAW POINTS STO Turns on a point.
Page 155 To erase (turn off) a drawn point on a graph, follow these steps. Erasing Points with Pt.Off( 1. Select (point off) from the menu. 2:Pt.Off( DRAW POINTS 2. Move the cursor to the point you want to erase. 3. Press Í to erase the point. To continue erasing points, repeat steps 2 and 3.
Page 156: Drawing Pixels
Drawing Pixels A pixel is a square dot on the TI-82 STATS display. The TI-82 STATS Pxl. (pixel) instructions let you turn on, turn off, or reverse a pixel Pixels (dot) on the graph using the cursor. When you select a pixel...
Page 157: Storing Graph Pictures
DRAW you select an instruction from the menu, the DRAW STO TI-82 STATS returns to the home screen or the program editor. The picture and graph database instructions are not interactive. DRAW POINTS STO Stores the current picture. 1: StorePic Recalls a saved picture.
Page 158: Recalling Graph Pictures
, or ) of the picture variable from which you want to recall a picture. For example, if you enter , the TI-82 STATS will recall the picture stored to Pic3 PICTURE Note: You also can select a variable from the secondary menu (...
Page 159: Storing Graph Databases
, or ) of the variable to which you want to store the graph database. For example, if you enter , the TI-82 STATS will store the GDB7 Note: You also can select a variable from the secondary StoreGDB menu (...
Page 160: Recalling Graph Databases
). The variable is pasted next to 3. Press Í to replace the current with the recalled . The new graph is not plotted. The TI-82 STATS changes the graphing mode automatically, if necessary. To delete a from memory, use the...
Page 161 Split Screen Contents Getting Started: Exploring the Unit Circle ..........Using Split Screen ....................(Horizontal) Split Screen Horiz ..............(Graph-Table) Split Screen ..............TI-82 STATS Pixels in Mode Horiz ........Split Screen 9–1...
Page 162: Getting Started: Exploring The Unit Circle
Getting Started: Exploring the Unit Circle Getting Started is a fast-paced introduction. Read the chapter for details. (graph-table) split-screen mode to explore the unit circle and its relationship to the numeric values for the commonly used trigonometric angles of 0 , 30 , 45 , 60 , 90 , and so on.
Page 163: Using Split Screen
If you press ], the cursor is placed in the half in which the table is TABLE displayed. The TI-82 STATS will remain in split-screen mode until you change back to screen mode. Full...
Page 164: Horiz (Horizontal) Split Screen
Horiz (Horizontal) Split Screen (horizontal) split-screen mode, a horizontal line splits Horiz Mode Horiz the screen into top and bottom halves. The top half displays the graph. The bottom half displays any of these editors. Home screen (four lines) editor (four lines) Stat list editor (two rows) Window editor (three settings) Table editor (two rows)
Page 165: G-T (Graph-Table) Split Screen
G.T (Graph-Table) Split Screen (graph-table) split-screen mode, a vertical line splits the G.T Mode screen into left and right halves. The left half displays the graph. The right half displays the table. To use the left half of the split screen: Moving from Half to Half in G.T Press s or r.
Page 166: Ti-82 Stats Pixels In Horiz And G.t Modes
TI-82 STATS Pixels in Horiz and G.T Modes TI-82 STATS Pixels in Horiz and G.T Modes Note: Each set of numbers in parentheses above represents the row and column of a corner pixel, which is turned on. , and DRAW POINTS Pxl.On(...
Page 167 Matrices Contents Getting Started: Systems of Linear Equations ........Defining a Matrix ....................Viewing and Editing Matrix Elements ............Using Matrices with Expressions ..............Displaying and Copying Matrices ..............Using Math Functions with Matrices ............Using the Operations MATRX MATH ............
Page 168: Getting Started: Systems Of Linear Equations
Getting Started is a fast-paced introduction. Read the chapter for details. Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-82 STATS, you can solve a system of linear equations by entering the coefficients as elements in a matrix, and then using to obtain the reduced row-echelon form.
Page 169: Defining A Matrix
Defining a Matrix A matrix is a two-dimensional array. You can display, define, or What Is a Matrix? edit a matrix in the matrix editor. The TI-82 STATS has 10 matrix variables, through . You can define a matrix directly in an expression. A matrix, depending on available memory, may have up to 99 rows or columns.
Page 170: Viewing And Editing Matrix Elements
Viewing and Editing Matrix Elements After you have set the dimensions of the matrix, you can view Displaying Matrix the matrix and enter values for the matrix elements. In a new Elements matrix, all values are zero. Select the matrix from the menu and enter or MATRX EDIT accept the dimensions.
Page 171 The matrix editor has two contexts, viewing and editing. In Viewing a Matrix viewing context, you can use the cursor keys to move quickly from one matrix element to the next. The full value of the highlighted element is displayed on the bottom line. Select the matrix from the menu, and then enter or MATRX EDIT...
Page 172 Viewing and Editing Matrix Elements (continued) In editing context, an edit cursor is active on the bottom line. To Editing a Matrix edit a matrix element value, follow these steps. Element 1. Select the matrix from the menu, and then MATRX EDIT enter or accept the dimensions.
Page 173: Using Matrices With Expressions
Using Matrices with Expressions To use a matrix in an expression, you can do any of the Using a Matrix in following. an Expression Copy the name from the menu. MATRX NAMES Recall the contents of the matrix into the expression with ] (Chapter 1).
Page 174: Displaying And Copying Matrices
Displaying and Copying Matrices To display the contents of a matrix on the home screen, select Displaying a the matrix from the menu, and then press Matrix MATRX NAMES Í. Ellipses in the left or right column indicate additional columns. in the right column indicate additional rows.
Page 175: Using Math Functions With Matrices
Using Math Functions with Matrices You can use many of the math functions on the TI-82 STATS Using Math keyboard, the menu, the menu, and the Functions with MATH MATH NUM MATH menu with matrices. However, the dimensions must be...
Page 176 Using Math Functions with Matrices (continued) (absolute value, menu) returns a matrix abs( abs( MATH NUM containing the absolute value of each element of matrix. matrix abs( menu) returns a matrix. It rounds every round( round( MATH NUM element in matrix to #decimals ( 9). If #decimals is omitted, the elements are rounded to 10 digits.
Page 177 To compare two matrices using the relational operations Relational ƒ menu), they must have the same dimensions. Operations TEST ƒ compare matrixA and matrixB on an element-by-element basis. The other relational operations are not valid with matrices. matrixA matrixB returns if every comparison is true;...
Page 178: Using The Matrx Math Operations
Using the MATRX MATH Operations menu, press  ~. To display the MATRX MATH MATRX MATH Menu NAMES MAT EDIT Calculates the determinant. 1: det( Transposes the matrix. Returns the matrix dimensions. 3: dim( Fills all elements with a constant. 4: Fill( Returns the identity matrix.
Page 179 with ¿ to create a new matrixname of dimensions Creating a Matrix dim( rows × columns with as each element. with dim( }! ! ! ! dim( rows columns matrixname with ¿ to redimension an existing matrixname to Redimensioning a dim( dimensions rows ×...
Page 180 Using the MATRX MATH Operations (continued) appends matrixA to matrixB as new columns. matrixA augment( augment( and matrixB both must have the same number of rows. matrixA matrixB augment( (matrix stored to list) fills each listname with elements Matr4list( Matr4list( from each column in matrix.
Page 181 returns cumulative sums of the elements in matrix, cumSum( cumSum( starting with the first element. Each element is the cumulative sum of the column from top to bottom. matrix cumSum( menu items through are row operations. You Row Operations MATRX MATH can use a row operation in an expression.
Page 182 Using the MATRX MATH Operations (continued) returns a matrix. It swaps rowA and rowB of matrix. rowSwap( rowSwap( matrix rowA rowB rowSwap( (row addition) returns a matrix. It adds rowA and rowB of row+( row+( matrix and stores the results in rowB. matrix rowA rowB...
Page 183 Lists Contents Getting Started: Generating a Sequence ..........Naming Lists ......................Storing and Displaying Lists ................Entering List Names ..................... Attaching Formulas to List Names .............. Using Lists in Expressions ................Menu LIST OPS ...................... Menu LIST MATH ....................Lists 11–1...
Page 184: Getting Started: Generating A Sequence
Getting Started: Generating a Sequence Getting Started is a fast-paced introduction. Read the chapter for details. Calculate the first eight terms of the sequence 1/A . Store the results to a user-created list. Then display the results in fraction form. Begin this example on a blank line on the home screen.
Page 185: Naming Lists
, or List: List1: List2: Freq: Freq1: Freq2: XList: prompt in the inferential stat editors YList: On the home screen using SetUpEditor You can create as many list names as your TI-82 STATS memory has space to store. Lists 11–3...
Page 186: Storing And Displaying Lists
Storing and Displaying Lists You can store list elements in either of two ways. Storing Elements to a List Use braces and ¿ on the home screen. Use the stat list editor (Chapter 12). The maximum dimension of a list is 999 elements. Tip: When you store a complex number to a list, the entire list is converted to a list of complex numbers.
Page 187 To copy a list, store it to another list. Copying One List to Another You can store a value to or recall a value from a specific list Accessing a List element. You can store to any element within the current list Element dimension or one element beyond.
Page 188: Entering List Names
Entering List Names menu, press y [ To display the ]. Each item is Using the LIST NAMES LIST a user-created list name. menu items are sorted LIST NAMES LIST NAMES automatically in alphanumerical order. Only the first 10 items are Menu labeled, using through...
Page 189: Attaching Formulas To List Names
Attaching Formulas to List Names You can attach a formula to a list name so that each list element Attaching a is a result of the formula. When executed, the attached formula Formula to a List must resolve to a list. Name When anything in the attached formula changes, the list to which the formula is attached is updated automatically.
Page 190 2. Press ¿. 3. Enter the name of the list to which you want to attach the formula. Press y, and then enter a TI-82 STATS list name through Press y [ ] and select a user.created list name from LIST menu.
Page 191: Using Lists In Expressions
Using Lists in Expressions You can use lists in an expression in any of three ways. When Using a List in an you press Í, any expression is evaluated for each list Expression element, and a list is displayed. – or any user-created list name in an expression.
Page 192: List Ops Menu
LIST OPS Menu menu, press y [ ] ~. To display the LIST OPS Menu LIST OPS LIST NAMESOPS MATH Sorts lists in ascending order. 1: SortA( Sorts lists in descending order. 2: SortD( Sets the list dimension. 3: dim( Fills all elements with a constant.
Page 193 (dimension) returns the length (number of elements) of list. Using dim( to dim( Find List list dim( Dimensions with ¿ to create a new listname with You can use Using dim( to dim( dimension length from 1 to 999. The elements are zeros. Create a List ! ! ! ! dim( length...
Page 194 LIST OPS Menu (continued) (sequence) returns a list in which each element is the result seq( seq( of the evaluation of expression with regard to variable for the values ranging from begin to end at steps of increment. variable need not be defined in memory. increment can be negative; the default value for increment is 1.
Page 195 Before using , follow these steps. Before Using Select( Select( 1. Create two list names and enter the data. " " " " Ó Ó Ó Ó 2. Turn on a stat plot, select (scatter plot) or (xyLine), and enter the two list names for (Chapter 12).
Page 196 LIST OPS Menu (continued) 6. Press Í. A indicator on the graph screen shows the left Using Select( to bound. is displayed in the bottom-left corner. Select Data Right Bound? Points from a Plot (continued) 7. Press | or ~ to move the cursor to the stat plot point that you want for the right bound, and then press Í.
Page 197 concatenates the elements of listA and listB. The list augment( augment( elements can be real or complex numbers. listA listB augment( (lists stored to matrix) fills matrixname column by List4matr( List4matr( column with the elements from each list. If the dimensions of all lists are not equal, then fills each extra matrixname List4matr(...
Page 198 Name= stat list editor or the prompts in the stat plot Xlist: Ylist: Ù Ù Ù Ù editor. If you enter where it is not necessary, the TI-82 STATS will ignore the entry. 11–16 Lists...
Page 199: List Math Menu
LIST MATH Menu menu, press y [ ] |. To display the LIST MATH Menu LIST MATH LIST NAMES Returns minimum element of a list. 1: min( Returns maximum element of a list. 2: max( Returns mean of a list. 3: mean( Returns median of a list.
Page 200 LIST MATH Menu (continued) (summation) returns the sum of the elements in list. start sum(, prod( sum( and end are optional; they specify a range of elements. list elements can be real or complex numbers. returns the product of all elements of list. start and end prod( elements are optional;...
Page 201 Statistics Contents Getting Started: Pendulum Lengths and Periods ........ Setting Up Statistical Analyses ..............Using the Stat List Editor .................. Attaching Formulas to List Names .............. Detaching Formulas from List Names ............Switching Stat List Editor Contexts ............Stat List Editor Contexts ..................
Page 202: Getting Started: Pendulum Lengths And Periods
Getting Started: Pendulum Lengths and Periods Getting Started is a fast-paced introduction. Read the chapter for details. A group of students is attempting to determine the mathematical relationship between the length of a pendulum and its period (one complete swing of a pendulum). The group makes a simple pendulum from string and washers and then suspends it from the ceiling.
Page 203 Ë Í to store the first 4. Press pendulum string length (6.5 cm) in . The rectangular cursor moves to the next row. Repeat this step to enter each of the 12 string length values in the table on page 12.2.
Page 204 Getting Started: Pendulum Lengths and Periods (cont.) Since the scatter plot of time-versus-length data appears to be approximately linear, fit a line to the data. 10. Press … ~ to select 4:LinReg(ax+b) (linear regression model) from the STAT menu. is pasted to the CALC LinReg(ax+b) home screen.
Page 205 The regression line appears to fit the central portion of the scatter plot well. However, a residual plot may provide more information about this fit. 14. Press … to select . The stat list 1:Edit editor is displayed. Press ~ and } to move the cursor onto Press y [ ].
Page 206 Getting Started: Pendulum Lengths and Periods (cont.) 18. Press y [ to select 2:Plot2 STAT PLOT from the menu. The stat plot STAT PLOTS editor is displayed for plot 2. 19. Press Í to select , which turns on plot 2. Press †...
Page 207 The residual pattern indicates a curvature associated with this data set for which the linear model did not account. The residual plot emphasizes a downward curvature, so a model that curves down with the data would be more accurate. Perhaps a function such as square root would fit.
Page 208 Getting Started: Pendulum Lengths and Periods (cont.) .522 The new function y=.192x appears to fit the data well. To get more information, examine a residual plot. 27. Press o to display the editor. Press | Í to deselect Press } Í to turn off plot 1. Press ~ Í...
Page 209 Now that you have a good model for the relationship between length and period, you can use the model to predict the period for a given string length. To predict the periods for a pendulum with string lengths of 20 cm and 50 cm, continue with these steps.
Page 210: Setting Up Statistical Analyses
Setting Up Statistical Analyses Data for statistical analyses is stored in lists, which you can Using Lists to create and edit using the stat list editor. The TI-82 STATS has Store Data six list variables in memory, through , to which you can store data for statistical calculations.
Page 211: Using The Stat List Editor
Using the Stat List Editor To enter a list name in the stat list editor, follow these steps. Entering a List Name in the Stat 1. Display the prompt in the entry line in either of two Name= List Editor ways.
Page 212 Using the Stat List Editor (continued) To create a name in the stat list editor, follow these steps. Creating a Name in the Stat List 1. Follow step 1 on page 12.11 to display the prompt. Name= Editor 2. Press [letter from A to Z or ] to enter the first letter of the name.
Page 213 To edit a list element, follow these steps. Editing a List Element 1. Move the rectangular cursor onto the element you want to edit. 2. Press Í to move the cursor to the entry line. Note: If you want to replace the current value, you can enter a new value without first pressing Í.
Page 214: Attaching Formulas To List Names
], enter the formula, and press ƒ [ ã ã Note: If you do not use quotation marks, the TI-82 STATS calculates and displays the same initial list of answers, but does not attach the formula for future calculations. Note: Any user-created list name referenced in a formula must be Ù...
Page 215 When a list with a formula attached is displayed in the stat list editor and you edit or enter elements of another displayed list, then the TI-82 STATS takes slightly longer to accept each edit or entry than when no lists with formulas attached are in view.
Page 216: Detaching Formulas From List Names
Editing an name is to edit an element of the list to which the formula is Element of a attached. The TI-82 STATS protects against inadvertently Formula- Generated List detaching the formula from the list name by editing an element of the formula-generated list.
Page 217: Switching Stat List Editor Contexts
Switching Stat List Editor Contexts The stat list editor has four contexts. Stat List Editor Contexts View-elements context Edit-elements context View-names context Enter-name context The stat list editor is first displayed in view-elements context. To switch through the four contexts, select from the 1:Edit menu and follow these steps.
Page 218: Stat List Editor Contexts
Stat List Editor Contexts In view-elements context, the entry line displays the list name, View-Elements the current element’s place in that list, and the full value of the Context current element, up to 12 characters at a time. An ellipsis ( indicates that the element continues beyond 12 characters.
Page 219 In view-names context, the entry line displays the list name and View-Names the list elements. Context To remove a list from the stat list editor, press {. Remaining lists shift to the left one column. The list is not deleted from memory.
Page 220: Stat Edit Menu
STAT EDIT Menu menu, press …. To display the STAT EDIT Menu STAT EDIT EDIT CALC TESTS Displays the stat list editor. 1: Edit... Sorts a list in ascending order. 2: SortA( Sorts a list in descending order. 3: SortD( Deletes all elements of a list.
Page 221 With you can set up the stat list editor to display SetUpEditor SetUpEditor one or more listnames in the order that you specify. You can specify zero to 20 listnames. [listname1 listname2 listname n] SetUpEditor with one to 20 listnames removes all list names SetUpEditor from the stat list editor and then stores listnames in the stat list editor columns in the specified order, beginning in column...
Page 222: Regression Model Features
Residual List becomes an item on the menu RESID RESID LIST NAMES (Chapter 11). The TI-82 STATS uses the formula below to compute RESID list elements. The next section describes the variable RegEQ = Ylistname N (Xlistname) RESID RegEQ...
Page 223 When you execute some regression models, the TI-82 STATS Diagnostics computes and stores diagnostics values for (correlation Display Mode coefficient) and (coefficient of determination) or for (coefficient of determination). are computed and stored for these regression models. LinReg(ax+b) LnReg PwrReg...
Page 224: Stat Calc Menu
Ù Ù Ù Ù FREQ={1,4,1,3} For example, if , then the ={15,12,9,14} Ù Ù Ù Ù FREQ TI-82 STATS interprets the instruction 1.Var Stats L to mean that occurs once, occurs four times, occurs once, and occurs three times.
Page 225 (one-variable statistics) analyzes data with one 1.Var Stats 1.Var Stats measured variable. Each element in freqlist is the frequency of occurrence for each corresponding data point in Xlistname. freqlist elements must be real numbers > 0. [Xlistname freqlist] 1.Var Stats (two-variable statistics) analyzes paired data.
Page 226 STAT CALC Menu (continued) (cubic regression) fits the third-degree polynomial CubicReg CubicReg y=ax +cx+d to the data. It displays values for , and +cx+d) ; when is set, it also displays a value for . For DiagnosticOn four points, the equation is a polynomial fit; for five or more, it is a polynomial regression.
Page 227 (power regression) fits the model equation y=ax to the PwrReg PwrReg data using a least-squares fit and transformed values ln(x) and ln(y). It displays values for ; when is set, it DiagnosticOn also displays values for [Xlistname Ylistname freqlist regequ] PwrReg fits the model equation y=c / (1+aäe ) to the data using...
Page 228 STAT CALC Menu (continued) Compute the regression model for the number of hours of SinReg Example: daylight in Alaska during one year. Daylight Hours in Alaska for One Year & & 1 period With noisy data, you will achieve better convergence results when you specify an accurate estimate for period.
Page 229: Statistical Variables
Statistical Variables The statistical variables are calculated and stored as indicated below. To access these variables for use in expressions, press , and select . Then select the 5:Statistics menu shown in the column below under menu. If you edit a list or VARS VARS change the type of analysis, all statistical variables are cleared.
Page 230: Statistical Analysis In A Program
Statistical Analysis in a Program You can enter statistical data, calculate statistical results, and fit Entering Stat models to data from a program. You can enter statistical data Data into lists directly within the program (Chapter 11). To perform a statistical calculation from a program, follow these Statistical steps.
Page 231: Statistical Plotting
Statistical Plotting You can plot statistical data that is stored in lists. The six types Steps for Plotting of plots available are scatter plot, xyLine, histogram, modified Statistical Data in box plot, regular box plot, and normal probability plot. You can Lists define up to three plots.
Page 232 Statistical Plotting (continued) Ò Ò Ò Ò plots one-variable data. The window variable Histogram Xscl value determines the width of each bar, beginning at (Histogram) Xmin adjusts , and to include all ZoomStat Xmin Xmax Ymin Ymax values, and also adjusts .
Page 233 Data List setting. Data Axis If you select , the TI-82 STATS plots the data on the x-axis and the z-values on the y-axis. If you select , the TI-82 STATS plots the data on the y-axis and the z-values on the x-axis.
Page 234 Statistical Plotting (continued) To define a plot, follow these steps. Defining the Plots 1. Press y [ ]. The menu is displayed STAT PLOTS STAT PLOT with the current plot definitions. 2. Select the plot you want to use. The stat plot editor is displayed for the plot you selected.
Page 235 Each stat plot has a unique stat plot editor. The name of the Displaying Other current stat plot ( , or ) is highlighted in the top Stat Plot Editors Plot1 Plot2 Plot3 line of the stat plot editor. To display the stat plot editor for a different plot, press }, ~, and | to move the cursor onto the name in the top line, and then press Í.
Page 236 Statistical Plotting (continued) Stat plots are displayed on the current graph. To define the Defining the viewing window, press p and enter values for the window Viewing Window variables. redefines the viewing window to display ZoomStat all statistical data points. When you trace a scatter plot or xyLine, tracing begins at the Tracing a Stat first element in the lists.
Page 237: Statistical Plotting In A Program
Statistical Plotting in a Program To display a stat plot from a program, define the plot, and then Defining a Stat display the graph. Plot in a Program To define a stat plot from a program, begin on a blank line in the program editor and enter data into one or more lists;...
Page 238 Statistical Plotting in a Program (continued) 5. Press ¢. Enter the list names, separated by commas. Defining a Stat Plot in a Program 6. Press ¢ y [ ] | to display the STAT PLOT (continued) menu. (This step is not necessary if you STAT PLOT MARK selected in step 4.)
Page 239 Inferential Statistics and Distributions Contents Getting Started: Mean Height of a Population ........Inferential Stat Editors ..................Menu STAT TESTS ..................... Inferential Statistics Input Descriptions ........... Test and Interval Output Variables .............. Distribution Functions ..................Distribution Shading ..................... Inferential Statistics and Distributions 13–1...
Page 240: Getting Started: Mean Height Of A Population
Getting Started: Mean Height of a Population Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to estimate the mean height of a population of women given the random sample below. Because heights among a biological population tend to be normally distributed, a t distribution confidence interval can be used when estimating the mean.
Page 241 4. Press … | to display the STAT TESTS menu, and then press † until 8:TInterval highlighted. 5. Press Í to select . The 8:TInterval inferential stat editor for TInterval displayed. If is not selected for Data Inpt: press | Í to select Data Press †...
Page 242 Getting Started: Mean Height of a Population (cont.) To obtain a more precise bound on the population mean of women’s heights, þ þ þ þ increase the sample size to 90. Use a sample mean of 163.8 and sample standard deviation of 7.1 calculated from the larger random sample (introduction;...
Page 243 11. Press to paste to the home screen. invNorm( Press Ë ¢ Ë ¢ Ë ¤ Í. is the area, is , and is . 165.1 6.35 The result is displayed on the home screen; it shows that five percent of the women are taller than 175.5 cm.
Page 244: Inferential Stat Editors
Inferential Stat Editors When you select a hypothesis test or confidence interval Displaying the instruction from the home screen, the appropriate inferential Inferential Stat statistics editor is displayed. The editors vary according to each Editors test or interval’s input requirements. Below is the inferential stat editor for T.Test ANOVA(...
Page 245 Arguments When you enter values in any inferential stat editor, the TI-82 STATS stores them in memory so that you can run many tests or intervals without having to reenter every value. Most of the inferential stat editors for the hypothesis tests Selecting an prompt you to select one of three alternative hypotheses.
Page 246 Inferential Stat Editors (continued) only) specifies whether Selecting the Pooled 2.SampTTest 2.SampTInt the variances are to be pooled for the calculation. Pooled Option Select if you do not want the variances pooled. Population variances can be unequal. Select if you want the variances pooled. Population variances are assumed to be equal.
Page 247: Stat Tests Menu
STAT TESTS Menu menu, press … |. When you To display the STAT TESTS STAT TESTS select an inferential statistics instruction, the appropriate Menu inferential stat editor is displayed. Most instructions store some output variables to STAT TESTS memory. Most of these output variables are in the TEST secondary menu ( menu;...
Page 248 STAT TESTS Menu (continued) (one-sample z test; item ) performs a hypothesis test for Z.Test Z.Test a single unknown population mean when the population standard deviation is known. It tests the null hypothesis : m=m against one of the alternatives below. : mƒm m:ƒm : m<m...
Page 249 (one-sample t test; item ) performs a hypothesis test for T.Test T.Test a single unknown population mean when the population standard deviation s is unknown. It tests the null hypothesis : m=m against one of the alternatives below. : mƒm m:ƒm : m<m m:<m...
Page 250 STAT TESTS Menu (continued) (two-sample z test; item ) tests the equality of 2.SampZTest 2.SampZTest the means of two populations (m and m ) based on independent samples when both population standard deviations (s are known. The null hypothesis H is tested against one of the alternatives below.
Page 251 (two-sample t test; item ) tests the equality of 2.SampTTest 2.SampTTest the means of two populations (m and m ) based on independent samples when neither population standard deviation (s or s ) is known. The null hypothesis H is tested against one of the alternatives below.
Page 252 STAT TESTS Menu (continued) (one-proportion z test; item ) computes a test for 1.PropZTest 1.PropZTest an unknown proportion of successes (prop). It takes as input the count of successes in the sample x and the count of observations in the sample n. tests the null hypothesis 1.PropZTest : prop=p...
Page 253 (two-proportion z test; item ) computes a test to 2.PropZTest 2.PropZTest compare the proportion of successes (p and p ) from two populations. It takes as input the count of successes in each sample (x and x ) and the count of observations in each sample and n tests the null hypothesis H 2.PropZTest...
Page 254 STAT TESTS Menu (continued) (one-sample z confidence interval; item ) computes a ZInterval ZInterval confidence interval for an unknown population mean m when the population standard deviation is known. The computed confidence interval depends on the user-specified confidence level. In the example: ={299.4 297.7 301 298.9 300.2 297} Data Stats...
Page 255 (one-sample t confidence interval; item ) computes a TInterval TInterval confidence interval for an unknown population mean m when the population standard deviation s is unknown. The computed confidence interval depends on the user-specified confidence level. In the example: ={1.6 1.7 1.8 1.9} Data Stats Input:...
Page 256 STAT TESTS Menu (continued) (two-sample z confidence interval; item 2.SampZInt 2.SampZInt computes a confidence interval for the difference between two population means (m ) when both population standard deviations ( ) are known. The computed confidence interval depends on the user-specified confidence level. In the example: LISTC={154 109 137 115 140} LISTD={108 115 126 92 146}...
Page 257 (two-sample t confidence interval; item 2.SampTInt 2.SampTInt computes a confidence interval for the difference between two population means (m ) when both population standard deviations ( ) are unknown. The computed confidence interval depends on the user-specified confidence level. In the example: SAMP1={12.207 16.869 25.05 22.429 8.456 10.589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.642} Data...
Page 258 STAT TESTS Menu (continued) (one-proportion z confidence interval; item 1.PropZInt 1.PropZInt computes a confidence interval for an unknown proportion of successes. It takes as input the count of successes in the sample x and the count of observations in the sample n. The computed confidence interval depends on the user-specified confidence level.
Page 259 (two-proportion z confidence interval; item 2.PropZInt 2.PropZInt computes a confidence interval for the difference between the proportion of successes in two populations (p ). It takes as input the count of successes in each sample (x and x ) and the count of observations in each sample (n and n ).
Page 260 STAT TESTS Menu (continued) (chi-square test; item ) computes a chi-square test for .Test .Test association on the two-way table of counts in the specified Observed matrix. The null hypothesis H for a two-way table is: no association exists between row variables and column variables.
Page 261 (two-sample Û-test; item ) computes an Û-test to 2.SampÜ Ü Ü Ü Test 2.SampÜ Ü Ü Ü Test compare two normal population standard deviations (s and s The population means and standard deviations are all unknown. 2.SampÜ Ü Ü Ü Test , which uses the ratio of sample variances /Sx2 , tests the null hypothesis H...
Page 262 STAT TESTS Menu (continued) (linear regression t test; item ) computes a linear LinRegTTest LinRegTTest regression on the given data and a t test on the value of slope b and the correlation coefficient r for the equation y=a+bx. It tests the null hypothesis H : b=0 (equivalently, =0) against one...
Page 263 (one-way analysis of variance; item ) computes a one- ANOVA( ANOVA( way analysis of variance for comparing the means of two to 20 populations. The procedure for comparing these means ANOVA involves analysis of the variation in the sample data. The null hypothesis H =...=m is tested against the alternative H...
Page 264: Inferential Statistics Input Descriptions
Specifies whether variances are to be pooled for Pooled 2.SampTTest instructs the TI-82 STATS not to pool the 2.SampTInt variances. instructs the TI-82 STATS to pool the variances. 13–26 Inferential Statistics and Distributions...
Page 265 Input Description The expected sample proportion for . Must be a 1.PropZTest real number, such that 0 < p < 1. The count of successes in the sample for the 1.PropZTest . Must be an integer ‚ 0. 1.PropZInt The count of observations in the sample for the 1.PropZTest .
Page 266: Test And Interval Output Variables
Test and Interval Output Variables The inferential statistics variables are calculated as indicated below. To access these variables for use in expressions, press , ), and then select the 5:Statistics menu listed in the last column below. VARS LinRegTTest, VARS Variables Tests Intervals...
Page 267: Distribution Functions
Distribution Functions menu, press y [ To display the DISTR menu DISTR DISTR DISTR DRAW Normal probability density 1: normalpdf( Normal distribution probability 2: normalcdf( Inverse cumulative normal distribution 3: invNorm( Student-t probability density 4: tpdf( Student-t distribution probability 5: tcdf( Chi-square probability density 6: c pdf(...
Page 268 Distribution Functions (continued) computes the normal distribution probability normalcdf( normalcdf( between lowerbound and upperbound for the specified mean and standard deviation . The defaults are lowerbound upperbound[ normalcdf( computes the inverse cumulative normal distribution invNorm( invNorm( function for a given area under the normal distribution curve specified by mean and standard deviation .
Page 269 computes the Student-t distribution probability between tcdf( tcdf( lowerbound and upperbound for the specified df (degrees of freedom), which must be > 0. lowerbound upperbound tcdf( computes the probability density function (pdf) for the c pdf( pdf( (chi-square) distribution at a specified x value. df (degrees of freedom) must be an integer >...
Page 270 Distribution Functions (continued) computes the probability density function (pdf) for the Û Ü Ü Ü Ü pdf( Ü Ü Ü Ü pdf( distribution at a specified x value. numerator df (degrees of freedom) and denominator df must be integers > 0. To plot the Û Ü...
Page 271 computes a probability at x for the discrete binomial binompdf( binompdf( distribution with the specified numtrials and probability of success (p) on each trial. x can be an integer or a list of integers. 0p1 must be true. numtrials must be an integer > 0. If you do not specify x, a list of probabilities from 0 to numtrials is returned.
Page 272 Distribution Functions (continued) computes a cumulative probability at x for the poissoncdf( poissoncdf( discrete Poisson distribution with the specified mean m , which must be a real number > 0. x can be a real number or a list of real numbers.
Page 273: Distribution Shading
Distribution Shading menu, press y [ ] ~ . To display the DISTR DRAW DISTR DRAW DISTR instructions draw various types of density Menu DISTR DRAW functions, shade the area specified by lowerbound and upperbound, and display the computed area value. To clear the drawings, select from the menu...
Page 274 Distribution Shading (continued) draws the density function for the Student-t Shade_t( Shade_t( distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound. lowerbound upperbound Shade_t( Note: For this example, Xmin = L3 Xmax = 3 Ymin = L.15 Ymax = .5 draws the density function for the c...
Page 275 Financial Functions Contents Getting Started: Financing a Car ..............Getting Started: Computing Compound Interest ........ Using the TVM Solver ..................Using the Financial Functions ................ Calculating Time Value of Money ( ..........Calculating Cash Flows ..................Calculating Amortization ................... Calculating Interest Conversion ..............
Page 276: Getting Started: Financing A Car
1. Press z † ~ ~ ~ Í to set the fixed-decimal mode setting to . The TI-82 STATS will display all numbers with two decimal places. 2. Press y [ ] to display the FINANCE menu.
Page 277: Getting Started: Computing Compound Interest
Getting Started: Computing Compound Interest At what annual interest rate, compounded monthly, will 1,250 accumulate to 2,000 in 7 years? Note: Because there are no payments when you solve compound interest problems, must be set to must be set to 1.
Page 278: Using The Tvm Solver
Using the TVM Solver displays the time-value-of-money ( Using the TVM TVM Solver variables. Given four variable values, the solves for Solver TVM Solver the fifth variable. menu section (page 14.14) describes the FINANCE VARS Ú Ú Ú Ú æ æ æ æ five variables ( , and...
Page 279: Using The Financial Functions
Using the Financial Functions When using the TI-82 STATS financial functions, you must Entering Cash enter cash inflows (cash received) as positive numbers and cash Inflows and Cash outflows (cash paid) as negative numbers. The TI-82 STATS Outflows follows this convention when computing and displaying answers.
Page 280: Calculating Time Value Of Money (Tvm)
14.4) or use ¿ and any FINANCE VARS variable on the menu (page 14.14). If you enter less than six arguments, the TI-82 STATS substitutes a previously stored variable value for each unspecified argument. If you enter any arguments with a function, you must place the argument or arguments in parentheses.
Page 281 tvm_æ æ æ æ tvm_æ æ æ æ computes the annual interest rate. Ú tvm_æ æ æ æ computes the present value. tvm_PV tvm_PV Ú æ tvm_PV tvm_Ú Ú Ú Ú tvm_Ú Ú Ú Ú computes the number of payment periods. æ...
Page 282: Calculating Cash Flows
Calculating Cash Flows Use the cash flow functions (menu items ) to analyze the Calculating a value of money over equal time periods. You can enter unequal Cash Flow cash flows, which can be cash inflows or outflows. The syntax descriptions for use these arguments.
Page 283: Calculating Amortization
It must be a positive integer < 10,000. roundvalue specifies the internal precision the calculator uses to calculate the balance; if you do not specify roundvalue, then the TI-82 STATS uses the current decimal-mode setting. Float...
Page 284 Calculating Amortization (continued) You want to buy a home with a 30-year mortgage at 8 percent Amortization APR. Monthly payments are 800. Calculate the outstanding loan Example: balance after each payment and display the results in a graph Calculating an and in the table.
Page 285 6. Press p to display the window variables. Enter the Amortization values below. Example: Calculating an Tmin=0 Xmin=0 Ymin=0 Outstanding Tmax=360 Xmax=360 Ymax=125000 Loan Balance Tstep=12 Xscl=50 Yscl=10000 (continued) 7. Press r to draw the graph and activate the trace cursor. Press ~ and | to explore the graph of the outstanding balance over time.
Page 286: Calculating Interest Conversion
Calculating Interest Conversion Use the interest conversion functions (menu items ) to Calculating an convert interest rates from an annual effective rate to a nominal Interest rate ( ) or from a nominal rate to an annual effective rate Conversion 4Nom( 4Eff( computes the nominal interest rate.
Page 287: Finding Days Between Dates/Defining Payment Method
Finding Days between Dates/Defining Payment Method Use the date function (menu item ) to calculate the dbd( dbd( number of days between two dates using the actual-day-count method. date1 and date2 can be numbers or lists of numbers within the range of the dates on the standard calendar. Note: Dates must be between the years 1950 through 2049.
Page 288: Using The Tvm Variables
Using the TVM Variables menu, press y [ ] ~. To display the FINANCE VARS FINANCE VARS FINANCE You can use variables in functions and store values to Menu them on the home screen. CALC VAR 1: Ú Total number of payment periods 2: æ...
Page 289 CATALOG, Strings, Hyperbolic Functions Contents Browsing the TI-82 STATS CATALOG ..........Entering and Using Strings ................Storing Strings to String Variables .............. String Functions and Instructions in the CATALOG ......Hyperbolic Functions in the CATALOG .........., Strings, Hyperbolic Functions 15–1...
Page 290: Browsing The Ti-82 Stats Catalog
Browsing the TI-82 STATS CATALOG is an alphabetical list of all functions and What Is the CATALOG instructions on the TI-82 STATS. You also can access each CATALOG? item from a menu or the keyboard, except: CATALOG The six string functions (page 15.6) The six hyperbolic functions (page 15.10)
Page 291: Entering And Using Strings
Entering and Using Strings A string is a sequence of characters that you enclose within What Is a String? quotation marks. On the TI-82 STATS, a string has two primary applications. It defines text to be displayed in a program.
Page 292: Strings
Storing Strings to String Variables The TI-82 STATS has 10 variables to which you can store String Variables strings. You can use string variables with string functions and instructions. To display the menu, follow these steps. VARS STRING 1. Press  to display the menu.
Page 293 To store a string to a string variable, follow these steps. Storing a String to a String 1. Press ƒ [ ], enter the string, and press ƒ [ ã ã Variable 2. Press ¿. 3. Press  to display the menu.
Page 294: String Functions And Instructions In The Catalog
String Functions and Instructions in the CATALOG String functions and instructions are available only from the Displaying String . The table below lists the string functions and Functions and CATALOG instructions in the order in which they appear among the other Instructions in menu items.
Page 295 converts to a string an equation that is stored to any Equ4String( Equ4String( variable. n contains the equation. n (from VARS Y.VARS , or ) is the string variable to which you want the Str1 Str9 Str0 equation to be stored as a string. Equ4String(Y ,Str converts the character string contained in string to an...
Page 296 String Functions and Instructions in the CATALOG (cont.) returns the number of characters in string. string can be length( length( a string or string variable. sin( cos( Note: An instruction or function name, such as , counts as one character. string length( converts string into an equation and stores the...
Page 297: Program Execution
returns a string that is a subset of an existing string. string sub( sub( can be a string or a string variable. begin is the position number of the first character of the subset. length is the number of characters in the subset. string begin length...
Page 298: Functions
Hyperbolic Functions in the CATALOG The hyperbolic functions are available only from the Hyperbolic CATALOG The table below lists the hyperbolic functions in the order in Functions which they appear among the other menu items. The CATALOG ellipses in the table indicate the presence of additional items.
Page 299 Programming Contents Getting Started: Volume of a Cylinder ............. Creating and Deleting Programs ..............Entering Command Lines and Executing Programs ......Editing Programs ....................Copying and Renaming Programs ............... (Control) Instructions PRGM CTL .............. (Input/Output) Instructions PRGM I/O ............. Calling Other Programs as Subroutines ...........
Page 300: Getting Started: Volume Of A Cylinder
Getting Started is a fast-paced introduction. Read the chapter for details. A program is a set of commands that the TI-82 STATS executes sequentially, as if you had entered them from the keyboard. Create a program that prompts for the radius R and the height H of a cylinder and then computes its volume.
Page 301 5. Press  ~ to select from the 3:Disp menu. is pasted to the PRGM I/O Disp command line. Press y [ ] ããä [ LOCK ] ããä ƒ ¢ ƒ ] Í to set up the program to display the text on one line and the calculated VOLUME IS...
Page 302: Creating And Deleting Programs
TI-82 STATS performs each instruction on each command line in the same order in which you entered them. The number and size of programs that the TI-82 STATS can store is limited only by available memory. To create a new program, follow these steps.
Page 303: Entering Command Lines And Executing Programs
) is updated during program execution. Last Entry is not updated as each command is executed (Chapter 1). The TI-82 STATS checks for errors during program execution. It does not check for errors as you enter a program. To stop program execution, press É. The...
Page 304: Editing Programs
Editing Programs To edit a stored program, follow these steps. Editing a Program 1. Press  ~ to display the menu. PRGM EDIT 2. Select a program name from the menu (page PRGM EDIT 16.7). Up to the first seven lines of the program are displayed.
Page 305: Copying And Renaming Programs
You can rename a program by copying its contents into a new program. Note: You also can copy all the command lines from one existing program to another existing program using The TI-82 STATS sorts menu Scrolling the PRGM EXEC PRGM EDIT items automatically into alphanumerical order.
Page 306: Prgm Ctl (Control) Instructions
To return to the program editor without selecting an item, press ‘. Program control instructions tell the TI-82 STATS which Controlling command to execute next in a program. , and...
Page 307 for testing and branching. If condition is false (zero), then the command immediately following is skipped. If condition is true (nonzero), then the next command is executed. instructions can be nested. condition command (if true) command Program Output following an executes a group of commands if condition If.Then Then...
Page 308 PRGM CTL (Control) Instructions (continued) following executes a group of commands if If.Then.Else Else If.Then condition is false (zero). identifies the end of the group of commands. condition :Then command (if true) command (if true) :Else command (if false) command (if false) :End command Program...
Page 309 performs a group of commands while condition is true. While While condition is frequently a relational test (Chapter 2). condition is tested when is encountered. If condition is true (nonzero), While the program executes a group of commands. signifies the end of the group.
Page 310 PRGM CTL (Control) Instructions (continued) identifies the end of a group of commands. You must include an instruction at the end of each , or For( While loop. Also, you must paste an instruction at the end Repeat of each group and each group.
Page 311 (label) and (go to) are used together for branching. Lbl, Goto Goto specifies the label for a command. label can be one or two characters ( through through , or label causes the program to branch to label when Goto Goto encountered.
Page 312 PRGM CTL (Control) Instructions (continued) (decrement and skip) subtracts 1 from variable. If the DS<( DS<( answer is < value (which can be an expression), the next command is skipped; if the answer is | value, the next command is executed. variable cannot be a system variable. variable value :DS<(...
Page 313 to execute other programs as subroutines (page prgm prgm 16.22). When you select , it is pasted to the cursor prgm location. Enter characters to spell a program name. Using prgm is equivalent to selecting existing programs from the PRGM menu;...
Page 314: Prgm I/O (Input/Output) Instructions
7: getKey Clears the display. 8: ClrHome Clears the current table. 9: ClrTable Gets a variable from another TI-82 STATS. 0: GetCalc( Gets a variable from CBL or CBR. A: Get( Sends a variable to CBL or CBR. B: Send( These instructions control input to and output from a program during execution.
Page 315 with variable displays a (question mark) prompt during Storing a Input execution. variable may be a real number, complex number, list, Variable Value matrix, string, or function. During program execution, enter with Input a value, which can be an expression, and then press Í. The value is evaluated and stored to variable, and the program resumes execution.
Page 316 PRGM I/O (Input/Output) Instructions (continued) During program execution, displays each variable, one Prompt Prompt at a time, followed by . At each prompt, enter a value or expression for each variable, and then press Í. The values are stored, and the program resumes execution. variableA[ variableB variable n]...
Page 317 (display graph) displays the current graph. If DispGraph DispGraph Pause is encountered after , the program halts temporarily DispGraph so you can examine the screen. Press Í to resume execution. (display table) displays the current table. The DispTable DispTable program halts temporarily so you can examine the screen. Press Í...
Page 318 Note: , , , and Í were pressed during program execution. Note: You can press É at any time during execution to break the program (page 16.5). TI-82 STATS Key Code Diagram ClrHome, (clear home screen) clears the home screen during ClrHome program execution.
Page 319 Get( Get( Note: If you transfer a program that references the command to the TI-82 STATS from a TI.82, the TI-82 STATS will interpret it as the Get( GetCalc( described above. Use to get data from another TI-82 STATS.
Page 320: Calling Other Programs As Subroutines
Calling Other Programs as Subroutines On the TI-82 STATS, any stored program can be called from Calling a another program as a subroutine. Enter the name of the program Program from to use as a subroutine on a line by itself.
Page 321 Applications Contents Comparing Test Results Using Box Plots ..........Graphing Piecewise Functions ............... Graphing Inequalities ................... Solving a System of Nonlinear Equations ..........Using a Program to Create the Sierpinski Triangle ......Graphing Cobweb Attractors ................Using a Program to Guess the Coefficients ...........
Page 322: Comparing Test Results Using Box Plots
Comparing Test Results Using Box Plots An experiment found a significant difference between boys and Problem girls pertaining to their ability to identify objects held in their left hands, which are controlled by the right side of their brains, versus their right hands, which are controlled by the left side of their brains.
Page 323 6. Press o. Turn off all functions. Procedure (continued) 7. Press p. Set . Press q Xscl=1 Yscl=0 select . This adjusts the viewing window and 9:ZoomStat displays the box plots for the women’s results. 8. Press r. Women’s left-hand data Women’s right-hand data Use | and ~ to examine , and...
Page 324: Graphing Piecewise Functions
Graphing Piecewise Functions The fine for speeding on a road with a speed limit of 45 Problem kilometers per hour (kph) is 50; plus 5 for each kph from 46 to 55 kph; plus 10 for each kph from 56 to 65 kph; plus 20 for each kph from 66 kph and above.
Page 325: Graphing Inequalities
Graphing Inequalities Graph the inequality 0 N 3X + 5 < 0 2X + 4. Use the Problem TEST menu operations to explore the values of X where the inequality is true and where it is false. 1. Press z. Select , and the default settings.
Page 326: Solving A System Of Nonlinear Equations
Solving a System of Nonlinear Equations Using a graph, solve the equation X N 2X = 2cos(X). Stated Problem another way, solve the system of two equations and two unknowns: Y = X N2X and Y = 2cos(X). Use factors to ZOOM control the decimal places displayed on the graph.
Page 327: Using A Program To Create The Sierpinski Triangle
Using a Program to Create the Sierpinski Triangle This program creates a drawing of a famous fractal, the Setting up the Sierpinski Triangle, and stores the drawing to a picture. To Program begin, press  ~ ~ . Name the program , and SIERPINS then press Í.
Page 328: Graphing Cobweb Attractors
Graphing Cobweb Attractors Using format, you can identify points with attracting and Problem repelling behavior in sequence graphing. 1. Press z. Select and the default mode settings. Press Procedure ]. Select format and the default format FORMAT settings. 2. Press o. Clear all functions and turn off all stat plots. Enter the sequence that corresponds to the expression Y = K X(1NX).
Page 329: Using A Program To Guess The Coefficients
Using a Program to Guess the Coefficients This program graphs the function A sin(BX) with random Setting Up the integer coefficients between 1 and 10. Try to guess the Program coefficients and graph your guess as C sin(DX). The program continues until your guess is correct.
Page 330: Graphing The Unit Circle And Trigonometric Curves
Graphing the Unit Circle and Trigonometric Curves Using parametric graphing mode, graph the unit circle and the Problem sine curve to show the relationship between them. Any function that can be plotted in mode can be plotted in Func mode by defining the component as and the component as F...
Page 331: Finding The Area Between Curves
Finding the Area between Curves Find the area of the region bounded by Problem f(x) = 300x / ( x + 625) g(x) = 3cos( = 75 1. Press z. Select the default mode settings. Procedure 2. Press p. Set the viewing window. Xmin=0 Ymin=L5 Xmax=100...
Page 332: Using Parametric Equations: Ferris Wheel Problem
Using Parametric Equations: Ferris Wheel Problem Using two pairs of parametric equations, determine when two Problem objects in motion are closest to each other in the same plane. A ferris wheel has a diameter (d) of 20 meters and is rotating counterclockwise at a rate (s) of one revolution every 12 seconds.
Page 333 4. Press s to graph the equations. Watch closely as they Procedure are plotted. Notice that the ball and the ferris wheel (continued) passenger appear to be closest where the paths cross in the top-right quadrant of the ferris wheel. 5.
Page 334: Demonstrating The Fundamental Theorem Of Calculus
Demonstrating the Fundamental Theorem of Calculus Using the functions from the menu to Problem 1 fnInt( nDeriv( MATH graph functions defined by integrals and derivatives demonstrates graphically that: ‰ F(x) = 1àt dt = ln(x), x > 0 and that [‰...
Page 335 Explore the functions defined by Problem 2 ‰ ‰ ‰ dt, and 1. Press o. Turn off all functions and stat plots. Use a list to Procedure 2 define these three functions simultaneously. Store the function in 2. Press q to select 6:ZStandard 3.
Page 336: Computing Areas Of Regular N-Sided Polygons
Computing Areas of Regular N-Sided Polygons Use the equation solver to store a formula for the area of a Problem regular N-sided polygon, and then solve for each variable, given the other variables. Explore the fact that the limiting case is the area of a circle, pr Consider the formula A = NB sin(pàN) cos(pàN) for the area...
Page 337 Find the area given , and , and Procedure N=10 1000 10000 Compare your results with p6 (the area of a circle with radius (continued) 6), which is approximately 113.097. 7. Enter . To find the area , move the cursor onto , and then press ƒ...
Page 338: Computing And Graphing Mortgage Payments
Computing and Graphing Mortgage Payments You are a loan officer at a mortgage company, and you recently Problem closed on a 30-year home mortgage at 8 percent interest with monthly payments of 800. The new home owners want to know how much will be applied to the interest and how much will be applied to the principal when they make the 240th payment 20 years from now.
Page 339 Now compare the graph of the amount of interest with the graph Procedure of the amount of principal for each payment. (continued) 4. Press z. Set Simul 5. Press o. Turn off all functions and stat plots. Enter these equations and set the graph styles as shown. FINANCE CALC Note: are located on the...
Page 340 Computing and Graphing Mortgage Payments (cont.) 8. Press † to move the cursor onto the function for interest Procedure defined by . Enter (continued) The graph shows that for the 240th payment ( ), 441.97 X=240 of the 800 payment is interest ( Y=441.97 9.
Page 341 Memory Management Contents Checking Available Memory ................Deleting Items from Memory ................. Clearing Entries and List Elements ............. Resetting the TI-82 STATS ................Memory Management 18–1...
Page 342: Checking Available Memory
2. Select to display the screen. The 1:Check RAM Check RAM TI-82 STATS expresses memory quantities in bytes. Note: The in the left column of the bottom row indicates that you can scroll or page down to view more variable types.
Page 343: Deleting Items From Memory
Deleting Items from Memory To increase available memory by deleting the contents of any Deleting an Item variable (real or complex number, list, matrix, variable, program, picture, graph database, or string), follow these steps. 1. Press y [ ] to display the menu.
Page 344: Clearing Entries And List Elements
Clearing Entries and List Elements clears the contents of the (last entry) Clear Entries Clear Entries ENTRY storage area (Chapter 1). To clear the storage area, ENTRY follow these steps. 1. Press y [ ] to display the menu. MEMORY 2.
Page 345: Resetting The Ti-82 Stats
It resets all system variables to the default settings. Tip: Before you reset all memory, consider restoring sufficient available memory by deleting only selected data (page 18 .3). To reset all memory on the TI-82 STATS, follow these steps. 1. Press y [ ] to display the menu.
Page 346 Resetting the TI-82 STATS (continued) When you reset defaults on the TI-82 STATS, all defaults are Resetting restored to the factory settings. Stored data and programs are not Defaults changed. These are some examples of TI-82 STATS defaults that are restored by resetting the defaults.
Page 347 Getting Started: Sending Variables ............. TI-82 STATS LINK ....................Selecting Items to Send ..................Receiving Items ....................... Transmitting Items ....................Transmitting Lists to a TI ................Transmitting from a TI 82 to a TI-82 STATS ........Backing Up Memory .................... Communication Link 19–1...
Page 348: Getting Started: Sending Variables
Getting Started: Sending Variables Getting Started is a fast-paced introduction. Read the chapter for details. Create and store a variable and a matrix, and then transfer them to another TI-82 STATS. 1. On the home screen of the sending unit, press Ë...
Page 349: Ti-82 Stats Link
Linking to a CBR to a TI-82 STATS with the unit-to-unit link cable. With a CBR or the CBL or a CBL and a TI-82 STATS, you can collect and analyze real- System world data. You can connect your TI-82 STATS to a personal computer Linking to a PC using TI Connect™...
Page 350: Selecting Items To Send
Displays all complex variables. 0: Complex... Displays all variables. A: Y-Vars... Displays all string variables. B: String... Selects all for backup to TI-82 STATS. C: Back Up... When you select an item on the menu, the LINK SEND corresponding screen is displayed.
Page 351: Receiving Items
Receiving Items menu, press y [ ] ~. To display the LINK RECEIVE LINK RECEIVE LINK Menu SEND RECEIVE Sets unit to receive data transmission. 1: Receive When you select from the menu on Receiving Unit 1:Receive LINK RECEIVE the receiving unit, the message and the busy indicator Waiting...
Page 352: Transmitting Items
The receiving unit is not set to receive transmission. You attempt a backup between a TI 82 and a TI-82 STATS. You attempt a data transfer from a TI-82 STATS to a TI with data other than lists through or without using...
Page 353 TI-82 STATS Note: You cannot repeat transmission if you selected All+ or All .. To transmit to an additional TI-82 STATS, follow these steps. 1. Set the TI-82 STATS to receive (page 19 2. Do not select or deselect any new items to send. If you select or deselect an item, all selections or deselections from the previous transmission are cleared.
Page 354: Transmitting Lists To A Ti
5. Confirm that the receiving unit is set to receive (page 19 6. Press Í to select and begin transmitting. 1:Transmit Note: If dimension > 99 for a TI-82 STATS list that is selected to send, the receiving TI 82 will truncate the list at the ninety-ninth element during transmission.
Page 355: Transmitting From A Ti - 82 To A Ti-82 Stats
Transmitting from a TI 82 to a TI-82 STATS Generally, you can transmit items to a TI-82 STATS from a Resolved 82, but differences between the two products may affect Differences some transmitted data. This table shows differences for which...
Page 356: Backing Up Memory
Backing Up Memory To copy the exact contents of memory in the sending Memory Backup TI-82 STATS to the memory of the receiving TI-82 STATS, put the other unit in receive mode. Then, on the receiving unit, select from the menu.
Page 357 Tables and Reference Information Contents Table of Functions and Instructions ............TI-82 STATS Menu Map .................. Variables ........................Statistics Formulas ....................Financial Formulas ....................Tables and Reference Information A–1...
Page 358: A-2 Tables And Reference Information
Table of Functions and Instructions Functions return a value, list, or matrix. You can use functions in an expression. Instructions initiate an action. Some functions and instructions have arguments. Optional arguments and accompanying commas are enclosed in brackets ( [ ] ). For details about an item, including argument descriptions and restrictions, turn to the page listed on the right side of the table.
Page 359 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item  matrixA matrixB Returns a matrix, which is matrixB augment( appended to matrixA as new MATH 10-14 columns. 7:augment( listA listB Returns a list, which is listB augment( LIST concatenated to the end of listA.
Page 360 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item pdf( Computes the probability density DISTR function (pdf) for the c DISTR distribution at a specified x value pdf( for the specified degrees of 13-31 freedom df.
Page 361 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item † y [ Turns off cursor coordinate value CoordOff FORMAT 3-14 display. CoordOff † y [ Turns on cursor coordinate value CoordOn FORMAT 3-14 display. CoordOn ™ value Returns cosine of a cos( real number, expression, or list.
Page 362 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item † z Degree Sets degree angle mode. 1-11 Degree †  variable Deletes from memory the DelVar contents of variable. 16-15 G:DelVar † y [ Sets table to ask for dependent- DependAsk TBLSET...
Page 363 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item †  Displays the graph. DispGraph 16-19 4:DispGraph †  Displays the table. DispTable 16-19 5:DispTable value Displays value in DMS format. 4DMS ANGLE ANGLE 2-24 4:4DMS † z Sets dot plotting mode;...
Page 364 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item †  Identifies end of For( , or Then Else Repeat While 16-12 loop. 7:End † z Sets engineering display mode. 1-10 Converts the contents of a Equ4String(Y= ,Str CATALOG...
Page 365 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item  expression variable Returns the value of variable fMax( lower upper[ tolerance] where the local maximum of MATH expression occurs, between lower 7:fMax( and upper, with specified tolerance.  expression variable Returns the value of variable...
Page 366 CBR and stores it in variable. 16-21 A:Get( †  variable Gets contents of variable on GetCalc( another TI-82 STATS and stores it 16-21 to variable on the receiving 0:GetCalc( TI-82 STATS. †  Returns the key code for the...
Page 367 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item †  function# Sets a graphstyle for function#. GraphStyle( graphstyle# H:GraphStyle( 16-15 † y [ Turns off grid format. GridOff FORMAT 3-14 GridOff † y [ Turns on grid format. GridOn FORMAT 3-14...
Page 368 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item † y [ IndpntAsk Sets table to ask for independent- TBLSET variable values. Indpnt: Ask † y [ Sets table to generate IndpntAuto TBLSET independent-variable values Indpnt: Auto...
Page 369 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item CFList[ CFFreq] Returns the interest rate at which irr( FINANCE the net present value of the cash CALC flows is equal to zero. 8:irr( 14-8 †  variable value Increments variable :IS>( by 1;...
Page 370 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item … LinReg(a+bx) [Xlistname Fits a linear regression model to Ylistname freqlist Xlistname and Ylistname with CALC regequ] frequency freqlist, and stores the 8:LinReg(a+bx) regression equation to regequ.
Page 371 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item … [Xlistname Fits a logistic regression model to Logistic Ylistname freqlist Xlistname and Ylistname with CALC regequ] frequency freqlist, and stores the B:Logistic regression equation to regequ. 12-27 matrix Fills each listname with elements Matr 4 list( LIST...
Page 372 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item  min( valueA valueB Returns smaller of valueA and valueB. 2-15 6:min( min( list Returns smallest real or complex LIST element in list. MATH 11-16 1:min(...
Page 373 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item lowerbound Computes the normal distribution normalcdf( DISTR upperbound[ probability between lowerbound DISTR and upperbound for the specified 2:normalcdf( 13-27 Computes the probability density normalpdf( DISTR function for the normal DISTR distribution at a specified x value 1:normalpdf(...
Page 374 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item †  Output( column ," text ") Displays text beginning at specified row and column. 16-19 6:Output( †  Output( column value Displays value beginning at specified row and column.
Page 375 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item Specifies an annuity due, where Pmt_Bgn FINANCE payments occur at the beginning CALC of each payment period. F:Pmt_Bgn 14-13 Specifies an ordinary annuity, Pmt_End FINANCE where payments occur at the end CALC 14-13 of each payment period.
Page 376 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item † … 1.PropZInt( Computes a one-proportion confidence level] z confidence interval. TESTS 13-20 A:1.PropZInt( † … 2.PropZInt( Computes a two-proportion confidence level] z confidence interval. TESTS 13-21 B:2.PropZInt(...
Page 377 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item column Reverses pixel at (row,column); Pxl.Change( DRAW ä 0  row  62 and POINTS 8-16 0  column  94. 6:Pxl.Change( column Erases pixel at (row,column); Pxl.Off( DRAW 0 ...
Page 378 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item  randInt( lower,upper Generates and displays a random [,numtrials] integer within a range specified by lower and upper integer 5:randInt( bounds for a specified number of 2-22 trials numtrials.
Page 379 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item †  condition Executes commands until :Repeat commands condition is true. 16-11 :End 6:Repeat commands †  Returns to the calling program. Return 16-15 E:Return  value[ #decimals] Returns a number, expression, round( list, or matrix rounded to 2-13...
Page 380 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item † … Performs a two-sample Û test. 2.SampÜ Ü Ü Ü Test [listname1 listname2 freqlist1 alternative= ; alternative= < TESTS D:2.SampÛ Û Û Û Test freqlist2 alternative ;...
Page 381 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item † … Computes a two-sample t test. 2.SampTTest alternative alternative= ; alternative= < TESTS pooled drawflag] ; alternative= . pooled= > 4:2.SampTTest ƒ (Summary stats input) pools variances; pooled= does not pool variances.
Page 382 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item †  Send( variable Sends contents of variable to the CBL System or CBR. 16-21 B:Send( seq( expression variable Returns list created by evaluating LIST begin end[...
Page 383 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item ShadeÜ Ü Ü Ü ( lowerbound Draws the density function for the DISTR Û upperbound distribution specified by DRAW 4:ShadeÜ Ü Ü Ü ( numerator df numerator df and denominator df denominator df and shades the area between lowerbound and upperbound.
Page 384 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item … SinReg [iterations Attempts iterations times to fit a Xlistname Ylistname sinusoidal regression model to CALC period regequ] Xlistname and Ylistname using a C:SinReg period guess, and stores the 12-27...
Page 385 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item Stores current picture in picture StorePic DRAW 8-17 1:StorePic string Converts string into an equation String4Equ( CATALOG and stores it in var. String4Equ( 15-8 string begin length Returns a string that is a subset of sub( CATALOG another string, from begin to...
Page 386 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item † y [ Time Sets sequence graphs to plot with FORMAT respect to time. Time † … [listname Computes a t confidence interval. TInterval freqlist confidence level]...
Page 387 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item Ú æ Computes the future value. tvm_FV FINANCE CALC 14-7 6:tvm_FV Ú tvm_æ æ æ æ Computes the annual interest rate. FINANCE CALC 3:tvm_æ æ æ æ 14-7 æ tvm_Ú...
Page 388 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item †  :While condition Executes commands while commands condition is true. 16-11 :End 5:While command valueA valueB Returns 1 if only valueA or TEST valueB = 0.
Page 389 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item † q Recalculates ZoomFit Ymin Ymax include the minimum and ZOOM maximum values, between 0:ZoomFit , of the selected Xmin Xmax functions and replots the 3-22 functions. † q Graphs the selected functions in a ZoomRcl user-defined viewing window.
Page 390 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item † … ZNTest( listname Performs a z test with frequency freqlist alternative freqlist. alternative= < TESTS drawflag] alternative= ; alternative= 1:Z.Test( ƒ (Data list input) .
Page 391 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item  root value Returns x root of value. ‡ MATH ‡  root list Returns x root of list elements. ‡ MATH ‡  list value Returns list roots of value. ‡...
Page 392 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item Greater than: Returns 1 if valueA > valueB. TEST valueA valueB Returns 0 if valueA  valueB. > TEST valueA and valueB can be real or 3:>...
Page 393 Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item › Powers: matrix power Returns matrix elements raised to 10-10 power. Ì Negation: value Returns the negative of a real or complex number, expression, list, 10-9 or matrix. Power of ten: value Returns 10 raised to the value power.
Page 394 Table of Functions and Instructions (continued) Function or Instruction/ Key or Keys/ Arguments Result Menu or Screen/Item Ã Addition: valueA valueB Returns valueA plus valueB. Ã Addition: list value Returns list in which value is added to each list element. Ã...
Page 395: Ti-82 Stats Menu Map
TI-82 STATS Menu Map The TI-82 STATS Menu Map begins at the top-left corner of the keyboard and follows the keyboard layout from left to right. Default values and settings are shown. (Func mode) (Par mode) (Pol mode) (Seq mode)
Page 396 TI-82 STATS Menu Map (continued) ZOOM MEMORY MEMORY 1:ZBox 1:ZPrevious (Set Factors...) 2:Zoom In 2:ZoomSto ZOOM FACTORS 3:Zoom Out 3:ZoomRcl XFact=4 4:ZDecimal 4:SetFactors… YFact=4 5:ZSquare 6:ZStandard 7:ZTrig 8:ZInteger 9:ZoomStat 0:ZoomFit FORMAT (Func/Par/Pol modes) (Seq mode) RectGC PolarGC Time Web uv vw uw...
Page 397 LINK SEND RECEIVE 1:All+… 1:Receive 2:AllN… 3:Prgm… 4:List… 5:Lists to TI82… 6:GDB… 7:Pic… 8:Matrix… 9:Real… 0:Complex… A:Y-Vars… B:String… C:Back Up… … EDIT CALC TESTS 1:Edit… 1:1-Var Stats 1:Z-Test… 2:SortA( 2:2-Var Stats 2:T-Test… 3:SortD( 3:Med-Med 3:2-SampZTest… 4:ClrList 4:LinReg(ax+b) 4:2-SampTTest… 5:SetUpEditor 5:QuadReg 5:1-PropZTest…...
Page 398 TI-82 STATS Menu Map (continued) LIST NAMES MATH 1:listname 1:SortA( 1:min( 2:listname 2:SortD( 2:max( 3:listname 3:dim( 3:mean( 4:Fill( 4:median( 5:seq( 5:sum( 6:cumSum( 6:prod( 7:@List( 7:stdDev( 8:Select( 8:variance( 9:augment( 0:List4matr( A:Matr4list( B:Ù Ù Ù Ù  MATH 1:4Frac 1:abs( 1:conj( 1:rand...
Page 399  ANGLE NAMES MATH EDIT ANGLE 1:[A] 1:det( 1:[A] 1:¡ 2:[B] 2:[B] 3: r 3:[C] 3:dim( 3:[C] 4:[D] 4:Fill( 4:[D] 4:4DMS 5:[E] 5:identity( 5:[E] 5:R4Pr( 6:[F] 6:randM( 6:[F] 6:R4Pq( 7:[G] 7:augment( 7:[G] 7:P4Rx( 8:[H] 8:Matr4list( 8:[H] 8:P4Ry( 9:[I] 9:List4matr( 9:[I] 0:[J] 0:cumSum( 0:[J]...
Page 400 TI-82 STATS Menu Map (continued) DRAW DRAW POINTS 1:ClrDraw 1:Pt-On( 1:StorePic 2:Line( 2:Pt-Off( 2:RecallPic 3:Horizontal 3:Pt-Change( 3:StoreGDB 4:Vertical 4:Pxl-On( 4:RecallGDB 5:Tangent( 5:Pxl-Off( 6:DrawF 6:Pxl-Change( 7:Shade( 7:pxl-Test( 8:DrawInv 9:Circle( 0:Text( A:Pen  VARS Y-VARS 1:Window… 1:Function… 2:Zoom… 2:Parametric… 3:GDB… 3:Polar… 4:Picture…...
Page 401 VARS (Zoom…) (Zoom…) (Zoom…) ZX/ZY ZT/Zq 1:ZXmin 1:ZTmin 1:Zu(nMin) 2:ZXmax 2:ZTmax 2:Zv(nMin) 3:ZXscl 3:ZTstep 3:Zw(nMin) 4:ZYmin 4:Zqmin 4:ZnMin 5:ZYmax 5:Zqmax 5:ZnMax 6:ZYscl 6:Zqstep 6:ZPlotStart 7:ZXres 7:ZPlotStep VARS (GDB…) (Picture…) GRAPH DATABASE PICTURE 1:GDB1 1:Pic1 2:GDB2 2:Pic2 9:GDB9 9:Pic9 0:GDB0 0:Pic0 VARS (Statistics…) (Statistics…)
Page 402 TI-82 STATS Menu Map (continued) VARS (Table…) (String…) TABLE STRING 1:TblStart 1:Str1 2:Str2 3:TblInput 3:Str3 4:Str4 9:Str9 0:Str0 Y-VARS (Function…) (Parametric…) (Polar…) (On/Off…) FUNCTION PARAMETRIC POLAR ON/OFF 1:FnOn 2:FnOff A–46 Tables and Reference Information...
Page 403 DISTR DISTR DRAW 1:normalpdf( 1:ShadeNorm( 2:normalcdf( 2:Shade_t( 3:invNorm( 3:Shadec 4:ShadeÛ Û Û Û ( 4:tpdf( 5:tcdf( pdf( cdf( 8:Û Û Û Û pdf( 9:Û Û Û Û cdf( 0:binompdf( A:binomcdf( B:poissonpdf( C:poissoncdf( D:geometpdf( E:geometcdf( FINANCE CALC VARS 1:TVM Solver… 1:Ú 2:tvm_Pmt 2:æ...
Page 404 TI-82 STATS Menu Map (continued) MEMORY MEMORY (Check RAM…) (Delete…) (Reset…) 1:Check RAM… MEM FREE 27225 DELETE FROM… RESET 2:Delete… Real 1:All… 1:All Memory… 3:Clear Entries Complex 2:Real… 2:Defaults… 4:ClrAllLists List 3:Complex… 5:Reset… Matrix 4:List… Y-Vars 5:Matrix… Prgm 6:Y-Vars… 7:Prgm…...
Page 405: Variables
The variables below must be real numbers. You may store to System Variables them. Since the TI-82 STATS can update some of them, as the result of a , for example, you may want to avoid using ZOOM these variables to store nongraphing data.
Page 406: Statistics Formulas
Statistics Formulas This section contains statistics formulas for the regressions, Logistic SinReg 2.SampÜ Ü Ü Ü Test , and ANOVA 2.SampTTest The logistic regression algorithm applies nonlinear recursive Logistic least-squares techniques to optimize the following cost function:   ∑ ...
Page 407 Û statistic is: ANOVA( ANOVA Factor MS Û Error MS The mean squares (MS) that make up Û are: Factor SS Factor MS Factor df Error SS Error MS Error df The sum of squares (SS) that make up the mean squares are: ∑...
Page 408 Statistics Formulas (continued) 2.SampÜ Ü Ü Ü Test SampÜ Ü Ü Ü Test Below is the definition for the Sx1, Sx2 = Sample standard deviations having n and n - 1 degrees of freedom df, respectively.   Û = Û -statistic = ...
Page 409 The following is the definition for the . The two- 2.SampTTest 2.SampTTest sample t statistic with degrees of freedom df is: where the computation of S and df are dependent on whether the variances are pooled. If the variances are not pooled: ...
Page 410: Financial Formulas
Financial Formulas This section contains financial formulas for computing time value of money, amortization, cash flow, interest-rate conversions, and days between dates. Time Value of Money where: PMT ƒ 0 y = C/Y x = (.01 C/Y = compounding periods per year P/Y = payment periods per year I% = interest rate per year where:...
Page 411 Time Value of   Money     (Continued) where: i ƒ 0 where: i = 0       where: i ƒ 0 where: i = 0       where: i ƒ...
Page 412: Financial Formulas
Financial Formulas (continued) If computing bal( ), pmt2 = npmt Amortization Let bal(0) = RND(PV) Iterate from m = 1 to pmt2  RND RND bal m  bal m bal m RND PMT  then: bal pm t Pr n bal pm t bal pm t In t...
Page 413 Cash Flow ∑ n pv  ∑  where: S    Net present value is dependent on the values of the initial cash flow (CF ), subsequent cash flows (CFj), frequency of each cash flow (nj), and the specified interest rate (i). irr( ) = 100 i, where i satisfies npv( ) = 0 Internal rate of return is dependent on the values of the initial...
Page 414 Financial Formulas (continued) With the function, you can enter or compute a date within Days between dbd( the range Jan. 1, 1950, through Dec. 31, 2049. Dates Actual/actual day-count method (assumes actual number of days per month and actual number of days per year): dbd( (days between dates) = Number of Days II - Number of Days I Number of Days I = (Y1...
Page 415 General Information Contents Battery Information ..............2 In Case of Difficulty...............4 Error Conditions..............5 Accuracy Information............10 Texas Instruments Support and Service........ 12 General Information B–1...
Page 416: To Replace Batteries
When the battery voltage level drops below a usable level, the TI-82 STATS displays this message when you turn on the unit. After this message is first displayed, you can expect the batteries to function for about one or two weeks, depending on usage.
Page 417 To replace the batteries, follow these steps. Replacing the Batteries 1. Turn off the calculator. Replace the slide cover over the keyboard to avoid inadvertently turning on the calculator. Turn the back of the calculator toward you. 2. Hold the calculator upright. Place your thumb on the oval indentation on the battery cover.
Page 418: In Case Of Difficulty
(Chapter 18). 4. If the busy indicator (dotted line) is displayed, a graph or program has been paused; the TI-82 STATS is waiting for input. Press Í to continue or press É to break. 5. If the calculator does not seem to work at all, be sure the batteries are fresh and that they are installed properly.
Page 419: Error Conditions
Error Conditions When the TI-82 STATS detects an error, it displays message and an error menu. ERR: Chapter 1 describes the general steps for correcting errors. This table contains each error type, possible causes, and suggestions for correction. Error Type...
Page 420 Duplicate Name because a variable with that name already exists in the receiving unit. ¦ The TI-82 STATS was unable to transmit an item. Check to Error in Xmit see that the cable is firmly connected to both units and that the receiving unit is in receive mode.
Page 421 Error Type Possible Causes and Suggested Remedies ¦ In mode, you attempted to graph a recursive sequence INVALID (cont.) without having input the correct number of initial conditions. ¦ In mode, you attempted to reference terms other than (nN1) (nN2) ¦...
Page 422 NONREAL ANS mode, the result of a calculation yielded a complex result. Real This error is not returned during graphing. The TI-82 STATS allows for undefined values on a graph. OVERFLOW You attempted to enter, or you have calculated, a number that is beyond the range of the calculator.
Page 423 ¦ Window variables are too small or too large to graph correctly. You may have attempted to zoom in or zoom out to a point that exceeds the TI-82 STATS numerical range. ZOOM ¦ A point or a line, instead of a box, is defined in ZBox.
Page 424: Accuracy Information
Accuracy Information To maximize accuracy, the TI-82 STATS carries more digits Computational internally than it displays. Values are stored in memory using up Accuracy to 14 digits with a two-digit exponent. You can store a value in the window variables using up to 10...
Page 425: Graphing Accuracy
Cursor coordinates are displayed as eight-character numbers Graphing (which may include a negative sign, decimal point, and Accuracy exponent) when mode is selected. are updated (continued) Float with a maximum accuracy of eight digits. on the menu are minimum maximum CALCULATE calculated with a tolerance of 1 is calculated at 1...
Page 426: Texas Instruments Support And Service
Home Page: For information about the length and terms of the warranty or Service and about product service, refer to the warranty statement enclosed warranty with this product or contact your local Texas Instruments information retailer/distributor. B–12 General Information...
Page 427 Index (addition), 2 3, A (absolute value), 2 13, 2 19, 10 abs( (chi-square cdf), 13 31, A cdf( (chi-square pdf), 13 31, A accuracy information pdf( (chi-square test), 13 22, A computational and graphing, B .Test (colon), 6, 16 graphing, 3 (concatenation), 15 6, A...
Page 428 Index (continued) Boolean logic, 2 (plotting mode), 1 11, A Connected box pixel mark ( ), 8 15, 12 contrast (display), 1 › Ö Ö Ö Ö plot type ( ), 12 convergence, sequence graphing, 6 Boxplot busy indicator, 1 conversions (to decimal), 2 5, A...
Page 429 cursors, 1 5, 1 , 13 31, A pdf( Û Û Û Û cdf( (compounding-periods-per-year , 13 32, A Û Û Û Û pdf( variable), 14 4, 14 , 13 32, A , 13 34, A geometcdf( . D . , 13 34, A geometpdf(...
Page 430 Index (continued) . D (continued) . errors diagnosing and correcting, 1 drawing on a graph messages, B circles ( ), 8 Circle( examples—applications functions and inverses ( DrawF area between curves, 17 ), 8 DrawInv areas of regular n-sided polygons, lines ( Horizontal Line(...
Page 431 . E (continued) . . F (continued) . examples—Getting Started (continued) (fixed-decimal mode), 1 10, A quadratic formula fixed-decimal mode ( ), 1 10, A converting to a fraction, 7 (floating-decimal mode), 1 10, A Float displaying complex results, 8 floating-decimal mode ( ), 1 10, A...
Page 432 34, A geometpdf( , 10 13, A identity( (get data from CBL or CBR), 16 Get( instructions , 16 9, A (get data from TI-82 STATS), GetCalc( , 16 9, A If-Then 21, A If-Then-Else , 16 10, A , 16...
Page 433 TI.82, 19 3, 19 4Nom( transmitting items, 19 12, A internal rate of return ( ), 14 8, A two TI-82 STATS units, 19 irr( operation on a graph, 3 menu, 19 intersect LINK RECEIVE menu, 19 inverse (...
Page 434 Index (continued) accessing an element, 11 inverse ( ), 10 attaching formulas, 11 7, 12 math functions, 10 9 – 10 clearing all elements, 12 12, 12 matrix math functions ( det( dim( copying, 11 Fill( identity( randM( augment( creating, 11 3, 12 Matr4list( List4matr(...
Page 435 (angle), 1 11, 2 24, A numerical integral, 2 7, 3 Degree (plotting), 1 11, A . O . (notation), 1 10, A (decimal), 1 10, A one-proportion z confidence interval ), 13 20, A (decimal), 1 10, A 1.PropZInt Float (screen), 1 12, A...
Page 436 Index (continued) , 12 34, A (sum of principal), 14 9, A Plot2( GPrn( , 12 34, A probability, 2 Plot3( , 12 35, A probability density function ( PlotsOff normalpdf( , 12 35, A 29, A PlotsOn plotting modes, 1 (product), 11 18, A prod(...
Page 437 (quartic regression), 12 , 10 16, A QuartReg row+( Quick Zoom, 3 19, A , 10 16, A …row( , 10 16, A …row+( . R . , 10 16, A rowSwap( (radian notation), 2 24, A (rectangular-to-polar R4Pr( R4Pq( (correlation coefficient), 12 conversions), 2 24, A...
Page 438 6 (sort descending), 11 10, 12 SortD( setting sequence mode, 6 selecting and deselecting, 6 split-screen modes TI-82 STATS versus TI.82 table, 6 (graph-table) mode, 9 tracing, 6 (horizontal) mode, 9 Horiz web plots, 6 setting, 9 3, 9...
Page 439 . S (continued) . (two-proportion 2.PropZInt z confidence interval), 13 statistical plotting, 12 (two-proportion z test), 2.PropZTest (regular box plot), 12 Boxplot defining, 12 (two-sample Û.Test), 2.SampÛ Û Û Û Test from a program, 12 , 12 Histogram (two-sample t confidence 2.SampTInt (modified box plot), ModBoxplot...
Page 440 4, 19 8, 19 transmitting TI-82 STATS error conditions, 19 features, 17, 18 from a TI.82 to a TI-82 STATS, 19 keyboard, 2, 3 items to another unit, 19 key code diagram, 16 lists to a TI.82, 19 4, 19 Link.
Page 441 . T (continued) . . V (continued) . turning on and off variables axes, 3 complex, 1 calculator, 1 displaying and storing values, 1 coordinates, 3 equation solver, 2 expressions, 3 graph databases, 1 functions, 3 graph pictures, 1 grid, 3 independent/dependent, 7 labels, 3 list, 1...
Page 442 Index (continued) . X . . Z (continued) . zoom factor, 3 (store zoom window), 3 XFact ZoomSto x-intercept of a root, 3 (Boolean) exclusive or operator, 2 (use previous window), 3 ZPrevious root ( ), 2 (set square pixels), 3 21, A ZSquare ‡...

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