Page 1
Chapter Statistical Graphs and Calculations This chapter describes how to input statistical data into lists, and how to calculate the mean, maximum and other statistical values. It also tells you how to perform regression calculations. Before Performing Statistical Calculations Calculating and Graphing Single-Variable Statistical Data Calculating and Graphing Paired-Variable Statistical Data...
6-1-1 Before Performing Statistical Calculations 6-1 Before Performing Statistical Calculations From the Main Menu, enter the STAT Mode and display the statistical data lists. Use the statistical data lists to input data and to perform statistical calculations. Use f, c, d and e to move the highlighting around the lists.
6-1-2 Before Performing Statistical Calculations k Changing Graph Parameters Use the following procedures to specify the graph draw/non-draw status, the graph type, and other general settings for each of the graphs in the graph menu (GPH1, GPH2, GPH3). While the statistical data list is on the display, press 1(GRPH) to display the graph menu, which contains the following items.
Page 4
6-1-3 Before Performing Statistical Calculations • Mark Type This setting lets you specify the shape of the plot points on the graph. u To display the general graph settings screen [GRPH]-[Set] Pressing 1(GRPH)f(Set) displays the general graph settings screen. • The settings shown here are examples only. The settings on your general graph settings screen may differ.
Page 5
6-1-4 Before Performing Statistical Calculations 2. Graph draw/non-draw status [GRPH]-[Select] The following procedure can be used to specify the draw (On)/non-draw (Off) status of each of the graphs in the graph menu. u To specify the draw/non-draw status of a graph 1.
6-2-1 Calculating and Graphing Single-Variable Statistical Data 6-2 Calculating and Graphing Single-Variable Statistical Data Single-variable data is data with only a single variable. If you are calculating the average height of the members of a class for example, there is only one variable (height). Single-variable statistics include distribution and sum.
Page 7
6-2-2 Calculating and Graphing Single-Variable Statistical Data k Med-box Graph (Box) This type of graph lets you see how a large number of data items are grouped within specific ranges. A box encloses all the data in an area from the 25th percentile to the 75th percentile, with a line drawn at the 50th percentile.
6-2-3 Calculating and Graphing Single-Variable Statistical Data k Normal Distribution Curve (N Dis) • The normal distribution curve is graphed using the following normal distribution function. ( x–x ) – 2xσ (2 π) xσ XList specifies the list where the data is input, while Freq specifies the list where the data frequency is input.
Page 9
6-2-4 Calculating and Graphing Single-Variable Statistical Data k Displaying the Calculation Results of a Drawn Single-Variable Graph Single-variable statistics can be expressed as both graphs and parameter values. When these graphs are displayed, the single-variable calculation results appear as shown below when you press 4(CALC)b(1VAR).
6-3-1 Calculating and Graphing Paired-Variable Statistical Data 6-3 Calculating and Graphing Paired-Variable Statistical Data k Drawing a Scatter Diagram and Line Graph Description The following procedure plots a scatter diagram and connects the dots to produce an line graph. Set Up 1.
Page 11
6-3-2 Calculating and Graphing Paired-Variable Statistical Data ○ ○ ○ ○ ○ Example Input the two sets of data shown below. Next, plot the data on a scatter diagram and connect the dots to produce an line graph. 0.5, 1.2, 2.4, 4.0, 5.2, –2.1, 0.3, 1.5, 2.0, 2.4 Procedure 1 m STAT...
6-3-3 Calculating and Graphing Paired-Variable Statistical Data k Drawing a Regression Graph Description Use the following procedure to input paired-variable statistical data, perform a regression calculation using the data, and then graph the results. Set Up 1. From the Main Menu, enter the STAT Mode. Execution 2.
Page 13
6-3-4 Calculating and Graphing Paired-Variable Statistical Data ○ ○ ○ ○ ○ Example Input the two sets of data shown below and plot the data on a scatter diagram. Next, perform logarithmic regression on the data to display the regression parameters, and then draws the corresponding regression graph.
Page 14
6-3-5 Calculating and Graphing Paired-Variable Statistical Data k k k k k Selecting the Regression Type After you graph paired-variable statistical data, press 4(CALC). Then you can use the function menu at the bottom of the display to select from a variety of different types of regression.
Page 15
6-3-6 Calculating and Graphing Paired-Variable Statistical Data k k k k k Linear Regression Graph Linear regression uses the method of least squares to plot a straight line that passes close to as many data points as possible, and returns values for the slope and y - intercept (y -coordinate when x = 0) of the line.
Page 16
6-3-7 Calculating and Graphing Paired-Variable Statistical Data k k k k k Quadratic/Cubic/Quartic Regression Graph A quadratic/cubic/quartic regression graph represents connection of the data points of a scatter diagram. It uses the method of least squares to draw a curve that passes close to as many data points as possible.
6-3-8 Calculating and Graphing Paired-Variable Statistical Data k Logarithmic Regression Graph Logarithmic regression expresses as a logarithmic function of . The standard logarithmic regression formula is × In , so if we say that X = In , the formula corresponds to linear regression formula 4(CALC)h(Log) 6(DRAW)
Page 18
6-3-9 Calculating and Graphing Paired-Variable Statistical Data k k k k k Power Regression Graph Power regression expresses as a proportion of the power of . The standard power regression formula is , so if we take the logarithms of both sides we get In = In ×...
Page 19
6-3-10 Calculating and Graphing Paired-Variable Statistical Data k k k k k Logistic Regression Graph Logistic regression is best applied for time-based phenomena in which there is a continual increase until a saturation point is reached. The following is the logistic regression model formula. 1 + ae –bx 4(CALC)l(Lgstic)
Page 20
6-3-11 Calculating and Graphing Paired-Variable Statistical Data k k k k k Displaying the Calculation Results of a Drawn Paired-Variable Graph Paired-variable statistics can be expressed as both graphs and parameter values. When these graphs are displayed, the paired-variable calculation results appear as shown below when you press 4(CALC)b(2VAR).
Page 21
6-3-12 Calculating and Graphing Paired-Variable Statistical Data k k k k k Multiple Graphs You can draw more than one graph on the same display by using the procedure under “Changing Graph Parameters” to set the graph draw (On)/non-draw (Off) status of two or all three of the graphs to draw On, and then pressing 6(DRAW)(see page 6-1-4).
6-3-13 Calculating and Graphing Paired-Variable Statistical Data k Overlaying a Function Graph on a Statistical Graph Description You can overlay a paired-variable statistical graph with any type of function graph you want. Set Up 1. From the Main Menu, enter the STAT Mode. Execution 2.
6-3-14 Calculating and Graphing Paired-Variable Statistical Data ○ ○ ○ ○ ○ Example Input the two sets of data shown below. Next, plot the data on a scatter diagram and overlay a function graph = 2ln 0.5, 1.2, 2.4, 4.0, 5.2, –2.1, 0.3, 1.5, 2.0, 2.4 Procedure 1 m STAT...
6-4-1 Performing Statistical Calculations 6-4 Performing Statistical Calculations All of the statistical calculations up to this point were performed after displaying a graph. The following procedures can be used to perform statistical calculations alone. u u u u u To specify statistical calculation data lists You have to input the statistical data for the calculation you want to perform and specify where it is located before you start a calculation.
Page 25
6-4-2 Performing Statistical Calculations k k k k k Single-Variable Statistical Calculations In the previous examples from “Drawing a Normal Probability Plot” and “Histogram (Bar Graph)” to “Line Graph,” statistical calculation results were displayed after the graph was drawn. These were numeric expressions of the characteristics of variables used in the graphic display.
6-4-3 Performing Statistical Calculations k Regression Calculation In the explanations from “Linear Regression Graph” to “Logistic Regression Graph,” regression calculation results were displayed after the graph was drawn. Here, each coefficient value of the regression line and regression curve is expressed as a number. You can directly determine the same expression from the data input screen.
6-4-4 Performing Statistical Calculations k Estimated Value Calculation ( , ) After drawing a regression graph with the STAT Mode, you can use the RUN MAT Mode to • calculate estimated values for the regression graph's parameters. ○ ○ ○ ○ ○ Example To perform power regression using the nearby data and estimate the values of...
6-4-5 Performing Statistical Calculations k Probability Distribution Calculation You can calculate probability distributions for single-variable statistics with the RUN • Mode. Press K6(g)1(PROB) to display a function menu, which contains the following items. • {P(}/{Q(}/{R(} ... obtains probability {P( )}/{Q( )}/{R( )} value •...
Page 29
6-4-6 Performing Statistical Calculations 1. Input the height data into List 1 and the frequency data into List 2. 2. Perform the single-variable statistical calculations. 2(CALC)e(Set) c2(LIST)cwi 2(CALC)b(1VAR) 3. Press m, select the RUN MAT menu, press K6(g)1(PROB), and recall the •...
Page 30
6-4-7 Performing Statistical Calculations k Drawing a Probability Distribution Graph Description You can draw a probability distribution graph using manual graphing with the RUN MAT Mode. • Set Up 1. From the Main Menu, enter the RUN MAT Mode. • Execution 2.
Page 31
6-4-8 Performing Statistical Calculations ○ ○ ○ ○ ○ Example To draw a probability P (0.5) graph. Procedure 1 m RUN • 2 K6(g)6(g)2(SKTCH)b(Cls)w 2(SKTCH)e(GRPH)b(Y=) 3 K6(g)1(PROB)f(P()a.fw Result Screen 19990401...