Datexx DS-991ES User Manual page 2

(Linear format) Calculation (Linear format)
Example Operation Result Example
√2 √5 = 3.65028154
sinh3.6= 18.28545536 [hyp] [1] [3] [.] [6] [ ) ] [=] 18.28545536
cosh1.23 = 1.856761057 [hyp] [2] [1] [.] [2] [3]
[ ) ] [=] 1.856761057 2 2 3 2 4 2 5 2 = 54
tanh2.5= 0.9866142982 [hyp] [3] [2] [.] [5] [ ) ] [=] 0.9866142982
cosh1.5 sinh1.5 [hyp] [2] [1] [.] [5] [ ) ] [ ] ( 3) 2 = 9
= 0.2231301601 [hyp] [1] [1] [.] [5] [ ) ] [=] 0.2231301601 1/(1/3–1/4) = 12
sinh –1 30 = 4.094622224 [hyp] [4] [3] [0] [ ) ] [=] 4.094622224
cosh –1 (20/15) [hyp] [5] [2] [0] [ ] (–3) 4 = 81
= 0.7953654612 [1] [5] [ ) ] [=] 0.7953654612
(tanh –1 0.88) / 4 [hyp] [6] [.] [8] [8] [ ) ] [ ] –3 4 = –81
2.3
= 0.3439419141 [4] [=] 0.3439419141 5.6 = 52.58143837
Degree, Radian, Gradient Interconversion
7 √(123) = 1.988647795
Degree, radian and gradient
r
1 : 0 2 :
can be converted to each other
3 : g
8! = 40320
with the use of [SHIFT] [Ans]
3 √(36 42 49) = 42
( i.e. DRG). After inputting
a value, press [SHIFT] [Ans] to display the angle unit
Abs (2 7) = 5
specification menu. Press the number key that corresponds to
the angle unit of the input value. The calculator will
Random number
automatically convert it to the calculator's default angle unit.
generation
E xample 1: To convert the following value to degrees:
π/4 = 45 º , 60 grads = 54 º , angle unit: Deg
Permutation and Combination
LINE
These functions make it possible to perform permutation and
x
combination calculations. n and r must be integers in the
[ ( ] [SHIFT] [x10 ] [ ] [4] [ ) ]
π r
( 4 ) range of 0 ≤ r ≤ n ≤ 1 10
[SHIFT] [Ans] [2] [=]
Total number of permutations nPr = n!/(n r)!
Total number of combinations nCr = n!/(r!(n r)!)
4 5
[6] [0] [SHIFT] [Ans] [3] [=]
g
6 0 / (Linear format)
Example
Taking any four out of
5 4
ten items and arranging
Example 2: cos(π radians) = –1 them in a row, how many
x
[cos] [SHIFT] [x10 ] different arrangements
π r
co s ( )
[SHIFT] [Ans] [2] [ ) ] [=]
are possible?
P = 5040
10 4
- 1
Using any four numbers
from 1 to 7, how many
Logarithmic and Exponential Functions
four digit even numbers
• For the logarithmic function ( [log] ), you can specify base m
can be formed if none of
using the format "log (m, n)" . Example: log
30 Press [log] [2]
2
the four digits consist of
[SHIFT] [ ) ] [3] [0] [ ) ] [=]
the same number?
If you input only a single value, base 10 is the default.
(3/7 of the total number
Example: log 16 Press [log] [1] [6] [ ) ] [=]
10
• [In] is a natural logarithm function with base e. of permutations will be
even.)
• In Math format you can also use the [log ] key when
P 3 7 = 360
inputting an expression with the form of "logmn" . However, 7 4
you must input the base (base m) when using the [log
If any four items are
]
removed from a total
function key.
of 10 items, how many
(Linear format) Calculation
different combinations
Example Operation Result
of four items are
log1.23 [log] [1] [.] [2] [3] [ ) ] [=] 0.08990511144
possible?
= 0.08990511144
10 C 4 = 210
In90 = 4.49980967 [In] [9] [0] [ ) ] [=] 4.49980967
If 5 class officers are
log456 In456 [log] [4] [5] [6] [ ) ] [ ]
being selected for a
= 0.4342944819 [In] [4] [5] [6] [ ) ] [=] 0.4342944819
class of 15 boys and
10 1.23 = 16.98243652 [SHIFT] [log] [1] [.] [2] [3]
10 girls, how many
[ ) ] [=] 16.98243652
combinations are
e
4.5 = 90.0171313 [SHIFT] [In] [4] [.] [5] [ ) ] [=] 90.0171313
possible? At least one
log 16 = 4 [log] [2] [SHIFT] [ ) ]
2
girl must be included
[1] [6] [ ) ] [=] 4
in each group.
MATH 25 C 5 15 C 5 = 50127
Math
l o g ( 1 6 )
log 16 = 4
2
2
[log ] [2] [] [1] [6] [=] Complex Number Calculation
• Press [MODE] [2]
4
calculations that include complex numbers.
Coordinate Transformation • In the CMPLX Mode, the [ENG] key changes function to
become an imaginary number i input key.
• This scientific calculator lets you convert between
rectangular coordinates and polar coordinates, i.e., P(x, y) ↔
MATH
Rec(r, )
Example
• Coordinate transformation can be performed in the COMP
and STAT calculation modes.
• Calculation results x and r are stored in variable memory X.
(2+3i)+(4+5i)
Calculation results y and are stored in variable memory Y.
• With polar coordinates, can be calculated within a range of Find the absolute value
–180 º < ≤ 180 º .
of (1+2i)
• If you perform coordinate transformation inside of an
Determine the argument
expression instead of a stand alone operation, the
(3+4i)
calculation is performed using only the first value (either the
r-value or the x-value) produced by the transformation.
• You can also input complex numbers using polar coordinate
--- ---
format (r ∠ ).
Example: Pol( 2, 2) 5 = 2 5 = 7 √ √
Example: To input 5∠30
(Linear format) Calculation
[5] [SHIFT] [ (–) ] [3] [0]
Example Operation Result
• The angle unit for argument
x=14 and y=20.7, what
Angle unit: Deg
calculator's default angle unit.
are r and º ?
[SHIFT] [ ] [1] [4] [SHIFT] r= 24.98979792
• At the end of the calculation, press [SHIFT] [2] [4] to specify
[ ) ] [2] [0] [.] [7] [ ) ] [=] =55.92839019
rectangular coordinate format for the calculation result.
x=7.5 and y=–10, what
Angle unit: Rad • At the end of the calculation, press [SHIFT] [2] [3] to specify
are r and rad?
[SHIFT] [ ] [7] [.] [5] polar coordinate format for the calculation result.
• To obtain a conjugate complex number press [SHIFT] [2] [2].
[SHIFT] [ ) ] [(–)] [1] [0] r= 12.5
Example: To determine the conjugate of the complex
[ ) ] [=] =–0.927295218
r=25 and = 56 º , what number 2+3i.
Angle unit: Deg
are x and y? [SHIFT] [2] [2] [2] [ ] [3] [i]
[SHIFT] [ ] [2] [5] [SHIFT] X=13.97982259
[ ) ] [=]
[ ) ] [5] [6] [ ) ] [=] Y=20.72593931
r=4.5 and =2π/3 rad,
Angle unit: Rad
what are x and y?
[SHIFT] [ ] [4] [.] [5]
Statistical Calculations
[SHIFT] [ ) ] [2] [SHIFT] X= –2.25
All calculations in this section are performed in the STAT
x
[x10 ] [ ] [3] [ ) ] [=] Y=3.897114317
Mode ( [MODE] [3] ).
MATH Press [MODE] [3] to display
r=25 and = 56 º , what are x and y? (Angle unit : Deg)
the STAT menu for statistical
[SHIFT] [ ] [2] [5] [SHIFT] calculation type selection.
Math
R e c ( 2 5 5 6 )
[ ) ] [5] [6] [ ) ] [=]
There are eight types of statistical calculations.
X = 1 3 9 7 9 8 2 2 5 9 Y Key Description
Press [] repeatedly until the
Math [1] Single variable (1-VAR)
R e c ( 2 5 5 6 )
right arrow disappears to show
[2] Linear regression (A+BX)
the full value of Y.
[3]
Quadratic regression (_+CX
 Y = 2 0 7 2 5 9 3 9 3 1
[4]
Logarithmic regression (In X)
e exponential regression (e
[5]
Integration Calculation
ab exponential regression (A•B
[6]
Integration calculation is performed using Gauss-Kronrod
[7] Power regression (A•X
method of numerical integration.
∫ ( f (x), a, b, tol ) [8] Inverse regression (1/X)
Inputting Sample Data
f (x): Function of X (all non-X variables are treated as Once you enter the STAT mode the STAT editor screen appears.
constants) Select a statistical calculation type by pressing the
a:
Integration interval lower limit corresponding number. To display the STAT editor screen from
b:
Integration interval upper limit another STAT mode screen, press [SHIFT] [1] [2].
tol:
Tolerance range (input / output format: Linear)
STAT Editor Screen
• Although a smaller tol value provides better precision, it
There are two STAT editor screen formats, depending on the
causes the calculation to take more time. Specify a tol value
type of statistical calculation you selected.
–14 –5
that is 1 10 or greater. A default value of 1 10 is used
STAT
| X |
when you omit specification of the tolerance range.
| |
1
| |
• Integration calculations can be performed in the COMP 2
| |
3
Mode only.
• Specify Rad as the calculator's default angle unit, when
Single-variable
performing an integration calculation involving
statistics
trigonometric functions. • The first line of the STAT editor screen shows the value for the
• Integration calculations can take considerable time to first sample or the values for their first pair samples and the
complete. second line shows the value of second sample and so on.
• You cannot input a tol value when using Math format.
• Errors may occur due to the type of function being Frequency Column
integrated, the presence of positive and negative values in A column labeled "FREQ" will also be included on the STAT
the integration interval, or the interval. editor screen if you turn on the Statistical Display item on the
calculator's setup screen. You can use the FREQ column to
Example: ∫ ( x –2 –7
, 5, 1, 1 10 ) = –0.8 specify the frequency of each sample value.
LINE
[∫ ] [ALPHA] [ ) ] [x ] [ (–) ] [2] Inputting Sample Data
( X ( - 2 ) 5 1 1 x
[ ) ] [SHIFT] [ ) ] [5] [SHIFT] [ ) ] • Data is inserted into the cell where the cursor is located. Use
[1] [SHIFT] [ ) ] [1] [x10 x ]
the cursor keys to move the cursor between cells.
[ (–) ] [7] [ ) ] [=] - 0 8 / • The values and expressions you can input on the STAT editor
screen are the same as those you can input in the COMP
Differential Calculation mode with Linear format.
Your calculator performs differential calculations by • Pressing [AC] while inputting data clears your current input.
approximating the derivative based on centered difference • After inputting a value, press [=] to confirm. This registers the
approximation. value but the cell can only display a maximum of 6 digits.
d/dx ( f (x), a, tol )
Example: To input the value 357 in cell X1, 8 in cell Y1.
f (x):
Function of X (all non-X variables are treated as [SHIFT] [1] [2]
constants) (to display the STAT
a:
Input a value to specify the point for which the editor screen)
derivative should be obtained (differential point)
tol:
Tolerance range (input / output format: Linear) [3] [5] [7]
(the value you input appears
• Inaccurate results and errors can be caused by the in the formula area)
following:-
- discontinuous points in x values
[=]
- extreme changes in x values
(registering a value causes the
- inclusion of the total maximum point and local minimum cursor to move down one cell)
point in x values
- inclusion of the inflection point in x values
[] [] [8] [=]
- inclusion of undifferentiable points in x values
- differential calculation results approaching zero
• Other limitations as stated for Integration Calculations also
applied in Differential Calculations.
Editing Sample Data in the STAT Editor Screen
Example: d/dx ( 3x
2 5x 2, 2, 1 10 –12 ) = 7 • Move the cursor to the cell you want to edit, input the new
LINE data or expression then press [=]. Note that you must totally
[SHIFT] [∫ ] [3] [ALPHA] [ ) ] replace the existing data of the cell with new input. You
2
d / d x ( 3 X - 5 X + 2 2
2
[x ][ ] [5] [ALPHA] [ ) ] [ ] [2] cannot edit part of the existing data.
[SHIFT] [ ) ] [2] [SHIFT] [ ) ] • To delete a line, move the cursor to the line you want to
x
[1] [x10 ] [ (–) ] [1] [2] [ ) ] [=] delete, press [DEL].
7
• To insert a line, move the cursor to the line that will be under
∑ Calculations
the line you will insert, press [SHIFT] [1] [3] [1]. The insert
With ∑(, you can obtain the sum of an input f(x) expression for operation will not work if the maximum number of lines
a specific range. ∑ calculaions are performed using the allowed for the STAT editor screen are already used.
following
∑ ( f (x), a, b ) = f (a) f (a 1) ...... f (b)
Deleting All Stat Editor Contents
Press [SHIFT] [1] [3] [2]
f (x):
Function of X (all non-X variables are treated as
constants) • You can only "insert a line" and "delete all stat editor contents"
a:
Calculation range start point when the STAT editor screen is on the display.
b:
Calculation range end point Notes
• The number of lines in STAT editor screen (the number of
• a and b are integers in the range of
sample data values you can input) depends on the type of
10 < a ≤ b < 1 10 10
–1 10 statistical data you selected, and on the "STAT" setting of the
• The calculation step is fixed at 1 calculator's setup screen.
• ∫(, d/dx(, Pol(, Rec(, and ∑( cannot be used within f (x), a or b
• To display the "STAT" setting screen press [SHIFT] [MODE]
[] [4].
Example: ∑ ( X 2, 1, 5 ) = 25
Math
Statistical
( X + 2 )
MATH
Type
X = 1 Display
[SHIFT] [log ] [ALPHA] [ ) ]
of Statistic
[ ] [2] [] [1] [] [5] [=] 2 5
Single-variable
Other Functions
Paired-variable
Factorial (!) function obtains the factorial of a value that is
zero or a positive integer.
Absolute Value Calculation (Abs) obtains the absolute value • The following types of input are not allowed on the STAT
when you are performing a real number calculation. editor screen: [M+] , [SHIFT] [M+] , [SHIFT] [RCL] (i.e. "STO").
Random Number (Ran#) generates a 3-digit pseudo random • When you change to another mode from the STAT mode or
number that is less than 1 (number is in the range of 0.000 to change the Statistical Display Setting (which enable or
0.999). Note that the values shown below are example only. disable the FREQ column) on the calculator's setup screen, all
Values actually generated by your calculator will be different. the sample data you input is deleted automatically.
STAT Calculation Screen
Calculation
Pressing the [AC] key while the STAT editor screen is displayed
Operation Result
_ _
switches to the STAT calculation screen to perform statistical
[ ] [2] [ ) ] [ ] [ ] [5]
√ √
calculations. This screen uses linear format regardless of the
[ ) ] [=] 3.65028154
current input/output format setting on the calculator's setup
[2] [x 2 ] [ ] [3] [x 2 ] [ ]
screen.
[4] [x 2 ] [ ] [5] [x 2 ] [=] 54
[ ( ] [(–)] [3] [ ) ] [x 2 ] [=] 9
STAT Menu
[ ( ] [3] [x –1 ] [ ] [4] [x –1 ]
While the STAT editor screen or STAT calculation screen is on
[ ) ] [x –1 ] [=] 12
the display, press [SHIFT] [1] to display the STAT menu. The
[ ( ] [(–)] [3] [ ) ] [x ] [4]
contents of the STAT menu for a single or paired variables are
[ ) ] [=] 81 different and are shown below:
[(–)] [3] [x ] [4] [ ) ] [=] –81
1 : T ype 2 : D ata 1 : Ty pe
[5] [.] [6] [x ] [2] [.] [3] 3 : S u m 4 : V a r 3 : S um
5 : D i s t r 6 : M i nM ax 5 : Reg
[ ) ] [=] 52.58143837
7 [SHIFT] [x ] [1] [2] [3] 1.988647795
Single-variable
[ ) ] [=]
statistics
–1
[8] [SHIFT] [x ] [=] 40320
_
The following tables explain the key function of the STAT
3
[SHIFT] [ √ ] [3] [6] [ ]
menu
[4] [2] [ ] [4] [9] [ ) ] [=] 42
Common items:
[SHIFT] [hyp] [2] [ ] [7] 5
Key Description
[ ) ] [=]
[1] (Type) Display the statistical calculation type
[SHIFT] [.] [=] 0.961
selection screen
[2] (Data) Display the STAT editor screen
[3] (Sum) Display the Sum sub-menu of
commands for calculating sums
[4] (Var) Display the Var sub-menu of commands
10 for calculating the mean, standard
.
deviation, etc.
[6] (MinMax) Display the MinMax sub-menu of
commands for obtaining maximum and
Calculation
minimum values
Operation Result
[1] [0] [SHIFT] [ ] [4] [=] 5040
The following is only available in the single-variable statistics
Key Description
[5] (Distr) Display the Distr sub-menu of commands
for normal distribution calculations
The following is only available in the paired-variable statistics
[7] [SHIFT] [ ] [4] [ ] [3] 360
Key Description
[ ] [7] [=]
[5] (Reg) Display the Reg sub-menu of commands
for regression calculations
Single-variable Statistical Calculation
The following are the commands that appear on the
sub-menus that appear when you select [3] (Sum), [4] (Var), or
[6] (MinMax) on the STAT menu while a single-variable
statistical calculation type is selected.
[1] [0] [SHIFT] [ ] [4] [=] 210
Standard deviation and mean calculations are performed as
shown below:
Population standard deviation xσn = √(∑(x i x) 2 /n)
where i = 1 to n
Sample standard deviation xσn–1 = √(∑(x i x) 2 /(n-1))
where i = 1 to n
Mean x = (∑x)/n
[2] [5] [SHIFT] [ ] [5] [ ]
Sum Sub-menu ( [SHIFT] [1] [3] )
[1] [5] [SHIFT] [ ] [5] [=] 50127
Key Description
2
[1] (∑x ) Sum of squares of the sample data
[2] (∑x) Sum of the sample data
Var Sub-menu ( [SHIFT] [1] [4] )
Key Description
[1] (n) Number of samples
[2] (x) Mean of the sample data
n
to enter the "CMPLX" mode for [3] (xσ ) Population standard deviation
n
σ
[4] (x ) Sample standard deviation
–1
MinMax Sub-menu ( [SHIFT] [1] [6] )
Key Description
Operation Display
[1] (min X) Minimum value
[MODE] [2] 0 [2] (max X) Maximum value
(CMPLX Mode)
i
[(] [2] [ ] [3] [ ] [)] [ ] [(] 6
i
[4] [ ] [5] [ ] [)] [=] +8i Example
i
√5
[SHIFT] [hyp] [1] [ ] [2] [ ] Use these data to calculate:
[=] Sum of squares of the sample data
i
Sum of the sample data
[SHIFT] [2] [1] [3] [ ] [4] [ ] 53.13010235
Number of samples
[)] [=]
Mean of the sample data
Population standard deviation
Sample standard deviation
Minimum value
CMPLX Math
5 / 3 0| | /
Maximum value
input and result display is the
Press [SHIFT] [MODE] [] [4] [1] to turn on the "Frequency
Column" .
Press [MODE] [3] [1] to select single-variable (1-VAR)
Input the data:
[5] [5] [=] [5] [4] [=] [5] [2] [=] [5] [1] [=] [5] [3] [=]
[] [] [2] [=] [2] [=] [] [] [2] [=]
Press [AC]
CMPLX
C o n j g ( 2 + 3 ii )
To calculate Operation
2
Sum of squares of the [SHIFT] [1] [3] [1] [=]
- 3 ii
sample data
Sum of the sample data [SHIFT] [1] [3] [2] [=]
Number of samples [SHIFT] [1] [4] [1] [=]
Mean of the sample [SHIFT] [1] [4] [2] [=]
data
1 : 1- VA R 2 : + X
A B
2 Population standard [SHIFT] [1] [4] [3] [=]
3 : - + C X 4 : I n X
5 : e X 6 : X
A B deviation
7 : A X B 8 : 1 / X
Sample standard [SHIFT] [1] [4] [4] [=]
deviation
Minimum value [SHIFT] [1] [6] [1] [=]
Maximum value [SHIFT] [1] [6] [2] [=]
Probability Distribution Calculation (Distr sub-menu)
2
)
You can calculate probabiltiy
1 : P (
distributions for single-variable
ˆ 3 : R (
X)
statistics by pressing [SHIFT]
ˆ
X)
[1] [5] in the STAT mode.
ˆ
B)
Input a value from 1 to 4 to select the probabilty distribution
calculation you want to perform.
P(t) Q(t)
X–x
t
X
=
x n
σ
Example: This table shows
STAT Height (cm) Frequency
| X | Y |
the results of measurements
| | |
1 158.5
| | |
2 of the height of 20 college
| | |
3 160.5
students. Determine what
163.3
percentage of the students
cursor Paired-variable
167.5
fall in the range of 160.5cm
statistics
170.2
to175.5cm. Also, in what
173.3
percentile does the 175.5cm
175.5
tall student fall?
178.6
Input the data using the 180.4
STAT Editor Screen with
186.7
the Frequency Column "ON"
Then you can perform the calculations.
To calculate Operation
Number of data [SHIFT] [1] [4] [1] [=]
Sum of data [SHIFT] [1] [3] [2] [=]
Sum of square data [SHIFT] [1] [3] [1] [=]
Mean [SHIFT] [1] [4] [2] [=]
Population SD [SHIFT] [1] [4] [3] [=]
Sample SD [SHIFT] [1] [4] [4] [=]
Normalized variate t [1] [6] [0] [•] [5] [SHIFT]
for 160.5cm. [1] [5] [4] [=]
Normalized variate t [1] [7] [5] [•] [5] [SHIFT]
for 175.5cm [1] [5] [4] [=]
STAT Percentage of the [SHIFT] [1] [5] [1]
| X | Y |
| | | students fall in the [1] [7] [5] [•] [5] [SHIFT]
1
| | |
2
| | | range 160.5 to 175.5cm [1] [5] [4] [ ) ] [ ]
3
[SHIFT] [1] [5] [1]
STAT
[1] [6] [0] [•] [5] [SHIFT]
| X | Y |
1 | | |
[1] [5] [4] [ ) ] [=]
| | |
2
| | |
3
3 5 7
Percentile of 175.5cm [SHIFT] [1] [5] [3]
STAT
| X | Y |
tall student [1] [7] [5] [•] [5] [SHIFT]
| | |
1 3 5 7 0
| | |
2 [1] [5] [4] [ ) ] [=]
| | |
3
STAT
| X | Y |
Commands when Linear Regression Calculation (A+BX) is
| | |
1 3 5 7 8
| | |
2 Selected
| | |
3
Linear regression calculations are carried out using the
following formula:
y = A + Bx.
The following are the commands that appear on the
sub-menus that appear when you select [3] (Sum), [4] (Var), [6]
(MinMax), or [5] (Reg) on the STAT menu while linear
regression is selected as the statistical calculation type.
Sum Sub-menu ( [SHIFT] [1] [3] )
Key Description
[1] (∑x 2 ) Sum of squares of the X-data
[2] (∑x) Sum of the X-data
2
[3] (∑y ) Sum of squares of the Y-data
[4] (∑y)
Sum of the Y-data
[5] (∑xy) Sum of products of the X-data and
Y-data
3
[6] (∑x ) Sum of cubes of the X-data
y)
2
[7] (∑x Sum of products of X-data squares and
Y-data
[8] (∑x 4 ) Sum of biquadrate of the X-data
Var Sub-menu ( [SHIFT] [1] [4] )
Key Description
[1] (n) Number of samples
OFF ON
[2] (x) Mean of the X-data
(FREQ column) (FREQ column)
σ n
[3] (x ) Population standard deviation of the
80 lines 40 lines
X-data
40 lines 26 lines σ n
[4] (x ) Sample standard deviation of the X-data
–1
[5] (y) Mean of the Y-data
n
σ
[6] (y ) Population standard deviation of the
Y-data
σ n
[7] (y ) Sample standard deviation of the Y-data
–1
MinMax Sub-menu ( [SHIFT] [1] [6] )
Key Description
[1] (min X) Minimum value of the X-data
[2] (max X)
Maximum value of the X-data
[3] (min Y) Minimum value of the Y-data
[4] (max Y) Maximum value of the Y-data
Reg Sub-menu ( [SHIFT] [1] [5] )
Key Description
[1] (A) Regression coefficient constant term A
[2] (B) Regression coefficient B
2 : Da ta
Correlation coefficient r
[3] (r)
4 : Var
6 : M i nM ax Estimated value of x
[4] (x)
Estimated value of y
[5] (y)
Paired-variable
statistics Example
Using this table, the regression
Temperature and
formula and correlation coefficient
length of a steel bar
can be obtained. Based on the
Temp Length
coefficient formula, the length of
10ºC 1003mm
the steel bar at 18ºC and the
15ºC 1005mm
temperature at 1000mm can be
20ºC 1010mm
estimated. Furthermore the critical
25ºC 1011mm
2
coefficient (r ) and covariance can
30ºC 1014mm
also be calculated.
Press [SHIFT] [MODE] [] [4] [2] to turn off the "Frequency
Column" .
Press [MODE] [3] [2] to select Linear regression (A+BX)
Input the data:
[1] [0] [=] [1] [5] [=] [2] [0] [=] [2] [5] [=] [3] [0] [=]
[] [] [1] [0] [0] [3] [=] [1] [0] [0] [5] [=]
[1] [0] [1] [0] [=] [1] [0] [1] [1] [=] [1] [0] [1] [4] [=]
Press [AC]
To calculate Operation Display
Regression coefficient [SHIFT] [1] [5] [1] [=]
constant term A
Regression coefficient B [SHIFT] [1] [5] [2] [=]
Correlation coefficient r
[SHIFT] [1] [5] [3] [=] 0.9826073689
Estimated value of x
[1] [0] [0] [0]
(temp at 1000mm) [SHIFT] [1] [5] [4] [=] 4.642857143
Estimated value of y
[1] [8]
(length at 18ºC) [SHIFT] [1] [5] [5] [=] 1007.48
Critical coefficient r
2 [SHIFT] [1] [5] [3] [x 2 ] [=] 0.9655172414
Covariance [ ( ] [SHIFT] [1] [3] [5] [ ]
[SHIFT] [1] [4] [1] [ ]
[SHIFT] [1] [4] [2] [ ]
[SHIFT] [1] [4] [5] [ ) ] [ ]
[ ( ] [SHIFT] [1] [4] [1] [ ]
[1] [ ) ] [=]
Commands when Quadratic Regression Calculation
2
(_+CX ) is Selected
Quadratic regression calculations are carried out using the
following formula:
y = A + Bx + Cx
2
Reg Sub-menu ( [SHIFT] [1] [5] )
Key Description
[1] (A) Regression coefficient constant term A
[2] (B) Linear coefficient B of the regression
coefficients
[3] (C) Quadratic coefficient C of the regression
coefficients
x x
[4] ( ) Estimated value of
1 1
x x
[5] ( ) Estimated value of
2 2
y y
[6] ( ) Estimated value of
• Sum sub-menu, Var sub-menu, and MinMax sub-menu
operations are the same as those for linear regression
calculations.
Example
Through quadratic regression of the xi yi
Data Frequency
these data, the regression formula
55 2
29 1.6
and correlation coefficient are
54 2
50 23.5
obtained. Furthermore, the
52 1
74 38
regression formula is used to
51 1
103 46.4
obtain the respective estimated
53 2 values of y and x, when
118 48
xi = 16 and yi = 20.
Press [SHIFT] [MODE] [] [4] [2] to turn off the "Frequency
Column" .
Press [MODE] [3] [3] to select Quadratic regression (_+CX
After using the method in the previous section to input the
data and now you can start the calculation.
To calculate Operation Display
Regression coefficient [SHIFT] [1] [5] [1] [=] –35.59856934
constant term A
Display
Regression coefficient B [SHIFT] [1] [5] [2] [=] 1.495939413
22805
Quadratic coefficient C [SHIFT] [1] [5] [3] [=] –6.71629667x10
Estimated value of x
[2] [0]
1
427 (when y = 20)
[SHIFT] [1] [5] [4] [=] 47.14556728
8 Estimated value of x
[2] [0]
2
53.375 (when y = 20)
[SHIFT] [1] [5] [5] [=] 175.5872105
Estimated value of y
[1] [6]
1.316956719 (when x = 16)
[SHIFT] [1] [5] [6] [=] –13.38291067
You can use the above operating procedure for other types of
1.407885953
regression.
51
Logarithmic Regression
55
Logarithmic regression calculations are carried out using the
following formula:
y = A + Blnx
2 : Q ( e Exponential Regression
4 :
e exponential regression calculations are carried out using the
following formula:
e Bx
y = A
ab Exponential Regression
R(t)
ab exponential regression calculations are carried out using
the following formula:
x
y = AB
Power Regression
Power regression calculations are carried out using the
following formula:
1 x
y = A
B
1
2
Inverse Regression
2
Power regression calculations are carried out using the
3
following formula:
4
y = A + ( B/x )
2
2
2 Comparison of Regression Curves
Using the data input in the
1 Temperature and
example under "Linear length of a steel bar
Regression Calculation" to
Temp Length
compare the correlation coefficient
10ºC 1003mm
for logarithmic, e exponential,
Display 15ºC 1005mm
ab exponential, power and
20ºC 1010mm
20.
inverse regression.
3440.1 25ºC 1011mm
592706.09 30ºC 1014mm
172.005
Correlation coefficient for logarithmic regression
7.041624457 Press [SHIFT] [1] [1]
STAT
r
7.224554257 (to select "Type")
Press [4] [AC]
[SHIFT] [1] [5] [3] [=]
-1.633855948
/ 0 9 7 7 6 1 2 6 7 8 5
Correlation coefficient for e exponential regression
0.4963343361
Press [SHIFT] [1] [1] [5] [AC]
STAT
r
[SHIFT] [1] [5] [3] [=]
/ 0 9 8 2 5 1 9 0 5 4 3 /
Correlation coefficient for ab exponential regression
Press [SHIFT] [1] [1] [6] [AC]
STAT
0.639025
r
[SHIFT] [1] [5] [3] [=]
(63.9%)
0 9 8 2 5 1 9 0 5 4 3 / /
Correlation coefficient for power regression
0.30983 Press [SHIFT] [1] [1] [7] [AC]
STAT
r
(31.0 percentile) [SHIFT] [1] [5] [3] [=]
0 9 7 7 7 4 4 8 5 3 5 /
Correlation coefficient for inverse regression
Press [SHIFT] [1] [1] [8] [AC]
STAT
r
[SHIFT] [1] [5] [3] [=]
- 0 9 4 6 1 4 7 3 0 7 8 /
Note: The commands included in the Reg sub-menu can take a
long time to execute in logarithmic, e exponential, ab
exponential, or power regression calculation when there are a
large number of data samples.
BASE-N Calculations
The BASE-N Mode lets you perform arithmetic calculations,
negative value calculations, and logical operations with binary,
octal, decimal, and hexadecimal values.
• Press [SHIFT] [3] to display page one of the BASE menu
which lets you to input a negative number or logical
operation command. Logical operations are performed
through logical products (and), logical sums (or), negative
(Not), exclusive logic sums (xor), and negation of exclusive
logical sums (xnor).
• Press [SHIFT] [3] [] to display page two of the BASE menu
which lets you specify the number base. The number system
(10 [DEC], 16 [HEX], 2 [BIN], 8 [OCT]) is set by pressing [1], [2],
[3], [4] respectively. A corresponding symbol "d", "h", "b" or
"o" appears on the display.
Example Operation Display
10111 11010 [BIN]
2 2
= 110001 [1] [0] [1] [1] [1] [ ]
2
[1] [1] [0] [1] [0] [=] 110001
B47 DF [HEX]
16 16
= A68 [B] [4] [7] [ ][D] [F] [=]
16
123 ABC = 37AF4 [OCT] [1] [2] [3] [=] [HEX]
8 16 16
= 228084 [ ] [A] [B] [C] [=]
10
[DEC]
228084
1F2D 100 = 7881 [HEX] [1] [F] [2] [D] [=] [DEC]
16 10 10
= 1EC9 [ ] [1] [0] [0] [=]
16
[HEX]
Example Operation Display
19 AND 1A = 18 [HEX] [1] [9] [SHIFT] [3] Hex
16 16 16
[1] [1] [A] [=] 18
1110 AND 36 = 1110 [BIN] [SHIFT] [3] [] [3]
2 8 2
[1] [1] [1] [0] [SHIFT] [3] [1]
[SHIFT] [3] [] [4] Bin
[3] [6] [=] 1110
23 OR 61 = 63 [OCT] [2 ] [3] Oct
8 8 8
[SHIFT] [3] [2] [6] [1] [=] 63
5 XOR 3 = 6 [HEX] [5] [SHIFT] [3] [3] Hex
16 16 16
[SHIFT] [3] [] [2] [3] [=] 6
2A XNOR 5D [HEX] [2] [A] [SHIFT] [3] [4] Hex
16 16
= FFFFFF88 [5] [D] [=] FFFFFF88
16
Not (1010 ) [BIN] [SHIFT] [3] [5] Bin
2
[1] [0] [1] [0] [)] [=] 1111111111110101
Negation of 1234 [OCT] [SHIFT] [3] [6]
8
[1] [2] [3] [4] [ )] [=] 37777776544
Equation Solving Function
All calculations in this section are performed in the "EQN
Mode" ( [MODE] [5] ).
Four choices are provided for users to select. Press the
corresponding number to select the type of equation.
[1] 2-unknown simultaneous linear equations
[2]
3-unknown simultaneous linear equations
[3] Quadratic equation
[4] Cubic equation
• After selecting the type of equation, a coefficient editor
screen appears. Input all the coefficient respectively to solve
the equation.
• You can use [] and [] to switch the display between the
solutions for X and Y (and Z) in simultaneous linear
equations. Likewise, you can use [] and [] to scroll the
display between X , X and X in quadratic or cubic equation.
1 2 3
The actual number of solutions depends on the equation.
997.4
Example :- To solve the quadratic equation x 2 2x 3=0
[MODE] [5] [3]
0.56
X =
[1] [=] [2] [=] [3] [=] 1
[=]
- 1
+ 1 . 4 1 4 2 1 3 5 6 2 ii
[]
X =
2
- 1
- 1 . 4 1 4 2 1 3 5 6 2 ii
35
Matrix Calculations
Press [MODE] [6] to select the MATRIX MODE. You can save
matrices under the names "MatA" , "MatB" , "MatC" in matrix
memory. Matrix calculation results are stored in a special
Matrix Answer Memory named "MatAns" .
• In the MATRIX mode,
M a t r i x ?
press [SHIFT] [4] [1] to
1 : Ma t A 2 : Ma t B
display the matrix selection
3 : Ma tC
screen.
Note that the matrix selection screen also appears whenever
you enter the MATRIX mode.
• Press [1], [2] or [3] to specify the name of the matrix you
want to select. This display a screen for configuring
dimension settings. Press [] to display the second page of
dimension settings.
M a t A ( m x n ) m x n ? M a t A ( m x n ) m x n ?
1 : 3x 3 2 : 3x2 1 : 1x 3 2 : 1 x2
3 : 3x 1 4 : 2 x3 3 : 1x 1
5 : 2 x2 6 : 2x 1
Press the corresponding number to specify the matrix
dimension you want to use and the matrix editor screen
appears.
• Use the matrix editor screen to input each of the elements
into the matrix.
• If you want to create another matrix, repeat the above
procedure.
To copy the contents of one Matrix to another Matrix
• Use the matrix editor screen to
Destination Press
display the matrix you want to
Matrix A [ (–) ]
copy, or display the Matrix Answer
Matrix B [ º''' ]
Memory screen. For example, if
Matrix C [hyp]
you want to copy Matrix A, press
[SHIFT] [4] [2] [1] then press [SHIFT] [RCL]. This causes the
"STO" indicator to appear on the display. Specify the
destination to store the matrix.
• The following are the menu items on the matrix menu that
appears when you press [SHIFT] [4].
Key Description
[1] (Dim) Select a matrix and specify its dimension
[2] (Data)
Select a matrix and display its data
[3] (MatA) Input "MatA"
2
)
[4] (MatB) Input "MatB"
[5] (MatC) Input "MatC"
[6] (MatAns) Input "MatAns"
[7] (det) Input the "det(" function for obtaining
the determinant
[8] (Trn) Input the "Trn(" function for obtaining
a transposed data in Matrix
–3
How to perform matrix calculation
Example: To multiply Matrix A by Matrix B, where
1 2
Matrix A = 4 0
–2 5
–1 0 3
Matrix B =
2 –4 1
First, define Matrix A
Press [SHIFT] [4] [1] [1] to select MatA
Input [2] to specify its dimension (MatA is a 3 2 matrix)
Then input all the elements for MatA:-
[1] [=] [2] [=] [4] [=] [0] [=] [–] [2] [=] [5] [=] [AC]
Second, define Matrix B
Press [SHIFT] [4] [1] [2] to select MatB
Input [4] to specify its dimension (MatB is a 2 3 matrix)
Then input all the elements for MatB:-
[–] [1] [=] [0] [=] [3] [=] [2] [=] [–] [4] [=] [1] [=] [AC]
Press [SHIFT] [4] [3]
MAT
AnS
to select MatA.
3 -8 5
Then input [ ] -4 0 12
12 -20 -1
Press [SHIFT] [4] [4]
3
to select MatB.
Press [=] the answer screen appears.
Using MatA as an example, to obtain the inverse matrix select
–1
MatA then press [x ] [=]. To obtain the absolute value of each
element of Mat A, use the Abs function then select MatA:-
[SHIFT] [hyp] [SHIFT] [4] [3] [ ) ] [=]
For doing transpose and determinant, select "Trn" and "det"
respectively in the matrix menu.
Vector Calculations
Press [MODE] [8] to select the VECTOR MODE. You can save
vectors under the names "VctA" , "VctB" , "VctC" in vector
memory. Vector calculation results are stored in a special
Vector Answer Memory named "VctAns" .
• In the VECTOR mode,
V e c t o r ?
press [SHIFT] [5] [1] to
1 : Vc tA 2 : Vc tB
display the vector selection
3 : V ctC
screen.
Note that the vector selection screen also appears whenever
you enter the VECTOR mode.
• Press [1], [2] or [3] to specify
V c t A ( m ) m ?
the name of the vector you
1 : 3 2 : 2
want to select. This display
a screen for configuring
dimension settings. Press the corresponding number to
specify the vector dimension you want to use and the vector
editor screen appears.
• Use the vector editor screen to input each of the elements.
• If you want to create another vector, repeat the above
procedure.
• You can copy the contents of one vector to another using
the same procedure as described in the Matrix section.
• The following are the menu items on the vector menu that
appears when you press [SHIFT] [5].
Key Description
[1] (Dim) Select a vector and specify its dimension
[2] (Data) Select a vector and display its data
[3] (VctA) Input "VctA"
[4] (VctB) Input "VctB"
[5] (VctC) Input "VctC"
[6] (VctAns) Input "VctAns"
[7] (Dot) Input the "•" command for obtaining the
dot product of a vector
Example: Input VctA = (1, 2) and VctB = (3, 4)
To input VctA press [MODE] [8] [1] [2]
then press [1] [=] [2] [=]
To input VctB press [AC] [SHIFT] [5] [1] [2] [2]
/
then press [3] [=] [4] [=]
[AC]
To calculate: 3 VctA, press
VCT
[3] [ ] [SHIFT] [5] [3] [=] AnS
3 6
3
To calculate: VctB 3 VctA,
Using VctAns, press
[SHIFT] [5] [4] [ ] VCT
AnS
[SHIFT] [5] [6] [=] 0 -2
/ 0
To calculate: VctA•VctB, press
VCT
Vct A •Vc tB
[SHIFT] [5] [3] [SHIFT] [5] [7]
[SHIFT] [5] [4] [=]
1 1
To calculate: VctA VctB, press
[SHIFT] [5] [3] [ ] VCT
AnS
[SHIFT] [5] [4] [=]
0 0 -2
/ 0
Bin
Generating a Number Table from a Function
Hex
All calculations in this section are performed in the "TABLE
A68
Mode" ( [MODE] [7] ).
Hex
37AF4
Configuring a Number Table Generation Function
Dec
The procedure below configures the number table generation
function with the following settings. Input/output format :
Dec
linear format
7881
Hex
Function: f(x) = x
2 3x 3
1EC9
Start Value: 3, End Value: 7, Step Value: 2
Press [MODE] [7]
f ( X ) =||
(select "TABLE")
Input the function
[ALPHA] [ ) ] [x 2 ] [ ] [3]
f ( X ) =X 2 + 3 X + 3 ||
[ALPHA] [ ) ] [ ] [3]
After making sure the function is correct, press
[=]
S t a r t ?
This displays the start value
input screen. (Initial default
start value is 1) 1
Press [3] [=] to specify the
E n d ?
initial start value for this
example. This displays the
5
end value input screen. (Initial
default end value is 5)
Press [7] [=] to specify the
S t e p ?
end value for this example.
This displays the step value
1
input screen. (Initial
default step value is 1)
Press [2] [=] to specify the
| X | F(X) |
step value for this example.
| | |
1 3 2 1
| | |
2 5 4 3
A number table is generated.
| | |
3 7 7 3
3
Pressing the [AC] key returns to the function editor screen.
Function Types that are supported
• Except for the X variable, other variables (A, B, C, D, Y) and
independent memory (M) are all treated as values (the
current variable assigned to the variable or stored in
independent memory).
• Only variable X can be used as the variable of a function.
• An error occur when an End value is less than Start value and
therefore the number table is not generated.
• Executing a number generation table using a Start, End and
Step value combination that produces more than 30 x-values
causes an error. To avoid this, the specified Start, End, and
Step values should onlyproduce a maximum of 30 x-values.
• Certain functions and Start, End, Step value combinations can
cause number table generation to take a long time.
Number Table Screen
The number table screen shows x-values calculated using the
specified Start, End, and Step values, as well as the values
obtained when each x-value is substituted in the function f(x).
• Table contents cannot be edited. You can use the number
table screen for viewing values only.
• To returns to the function editor screen, press the [AC] key.
Note that in the Table Mode you should not change the
input/ouput format settings (Math format or Linear
format) otherwise the number table generation function is
cleared.
Scientific Constants
A total of 40 commonly used scientific constants, such as the
speed of light in a vaccum and Planck's constant are built-in for
quick and easy look-up. Simply press [SHIFT] [7] and the
number that corresponds to the scientific constant (see the
table below for a complete list of available constants) you want
to look-up and press [=], it appears instantly on the display.
Example:
C o
Press [SHIFT] [7] [2] [8] [=]
2 9 9 7 9 2 4 5 8
To select this constant Input this number
proton mass (mp) 01
neutron mass (mn) 02
electron mass (me) 03
muon mass (m ) 04
Bohr radius (a ) 05
0
Planck constant (h) 06
nuclear magneton ( N) 07
Bohr magneton ( B) 08
Planck constant, rationalized (h) 09
fine structure constant ( ) 10
classical electron radius (re) 11
Compton wavelenght ( c) 12
proton gyromagnetic ratio ( p) 13
proton Compton wavelength ( cp) 14
neutron Compton wavelength ( cn) 15
Rydberg constant (R ) 16
atomic mass unit (u) 17
proton magnetic moment ( p) 18
electron magnetic moment ( e) 19
neutron magnetic moment ( n) 20
muon magnetic moment ( ) 21
Faraday constant (F) 22
elementary charge (e) 23
Avogadro constant (NA) 24
Boltzmann constant (k) 25
molar volume of ideal gas (Vm) 26
molar gas constant (R) 27
speed of light in vaccum (C ) 28
0
first radiation constant (C ) 29
1
second radiation constant (C ) 30
2
31
Stefan-Boltzmann constant ( )
electric constant ( ) 32
0
magnetic constant ( ) 33
0
magnetic flux quantum ( ) 34
0
standard acceleration of gravity (g) 35
conductance quantum (G ) 36
0
characteristic impedance of vaccum (Z ) 37
0
Celsius temperature (t) 38
Newtonian constant of gravitation (G) 39
standard atmosphere (atm) 40
Metric Conversion
A total of 20 different conversion pairs are bulit-in to provide
quick and easy conversion to and from metric units. For details,
please refer to the following table.
Number Conversion Number Conversion
01 in cm 21 oz g
 
02 cm in 22 g oz
 
03 ft m 23 lb kg
 
04 m ft 24 kg lb
 
05 yd m 25 atm pa
 
06 m yd 26 pa atm
 
07 mile km 27 mmHg Pa
 
08 km mile 28 Pa mmHg
 
09 n mile m 29 hp kW
 
10 m n mile 30 kW hp
 
11 acre m 2 31 kgf/cm 2 Pa
 
12 m 2 acre 32 Pa kgf/cm 2
 
l
13 gal (US) 33 kgf•m J
 
l
14 gal (US) 34 J kgf•m
 
l
15 gal (UK) 35 lbf/in 2 kPa
 
l
16 gal (UK) 36 kPa lbf/in 2
 
17 pc km 37 º F º C
 
18 km pc 38 º C º F
 
19 km/h m/s 39 J cal
 
20 40
m/s  km/h cal  J
Example: To convert 31 inches to centimeters
[3] [1] [SHIFT] [8] [0] [1] [=]
3 1 i n c m
7 8 7 4
Trouble Shooting
Perform the following steps whenever an error occurs during a
calculation or when calculation results are not what you
expected. If one step does not correct the problem, move on to
the next step.
Note that you should make separate copies of important data
before performing these steps.
• Check the calculation expression to make sure that it does
not contain any errors.
• Make sure that you are using the correct mode for the type of
calculation you are trying to perform.
• If the above steps do not correct your problem, press the
[ON] key. This will cause the calculator to perform a routine
that checks whether calculation functions are operating
correctly. If the calculator discovers any abnormality, it
automatically initializes the calculation mode and clears
memory contents.
• Initialize all modes and settings by performing the following
operation:
[SHIFT] [9] [1] [=]
Replacing the Battery
Dim figures on the display of the calculator indicate that
battery power is low. Continued use of the calculator when the
battery is low can result in improper operation. Replace the
battery as soon as possible when display figures become dim.
To replace the battery:-
• Remove the two screws that hold the back cover in place and
then remove the back cover,
• Remove the old battery,
• Wipe off the side of the new battery with a dry, soft cloth.
Load it into the unit with the positive(+) side facing up.
• Replace the battery cover and secure it in place with the two
screws.
• Press [ON] to turn power on.
Auto Power Off
Calculator power automatically turns off if you do not perform
any operation for about six minutes. When this happens, press
[ON] to turn power back on.
Specifications
Power supply: single LR44 battery
Operating temperature: 0 º ~ 40 º C (32 º F ~ 104 º F)