This is the English chapter of the original user manual of the Casio fx-85v.
Scanned, transformed to ASCII via OCR and copied to HTML by F. Seebass, July 2002.
 


CASIO

fx-85v

Electronic Calculator

User Manual


Dear customer,

Thank you very much for purchasing our electronic calculator.
To fully utilize its features no special training is required, but we suggest you study this operation manual to become familiar with its many abilities. To help ensure its longevity, do not touch the inside of the calculator, avoid hard knocks and unduly strong key pressing. Extreme cold (below 32°F or 0°C heat (above 104°F or 40°C) and humidity may also affect the functions of the calculator. Never use volatile fluid such as lacquer thinner, benzine, etc. when cleaning the unit. For servicing contact your retailer or nearby dealer.

Before starting calculation, be sure to press the [ON]-key and to confirm that "0." is shown on the display.

* Special care should be taken not to damage the unit by bending or dropping. For example, do not carry it in your hip pocket.
 

INDEX

KEY INDEX

General keys
Memory keys
Special keys
Function keys
Statistical keys

1 / GENERAL GUIDE

1-1 Modes
1-2 The display

2 / ORDER OF OPERATIONS AND LEVELS

3 / CALCULATION RANGE AND SCIENTIFIC NOTATION

4 / CORRECTIONS

5 / OVERFLOW OR ERROR CHECK

6 / POWER SOURCE

7 / SPECIFICATIONS

8 / NORMAL CALCULATIONS

8-1 Four basic calculations (incl. parenthesis calculations)
8-2 Constant calculations
8-3 Memory calculations using the independent memory
8-4 Memory calculations using 6 constant memories
8-5 Fraction calculations
8-6 Percentage calculations

9 / FUNCTION CALCULATIONS

9-1 Sexagesimal <-> Decimal conversion
9-2 Trigonometric/Inverse trigonometric functions
9-3 Hyperbolic functions and inverse hyperbolic functions
9-4 Common & Natural logarithms/Exponentiations (Common antilogarithms, Natural antilogarithms, Powers and Roots)
9-5 Square roots, Cube roots, Squares, Reciprocals & Factorials
9-6 Miscellaneous functions (FIX, SCI, NORM, RND, RAN#, ENG)
9-7 Polar to rectangular co-ordinates conversion
9-8 Rectangular to polar co-ordinates conversion
9-9 Permutations
9-10 Combinations

10 / STATISTICAL CALCULATIONS

10-1 Standard deviation
10-2 Regression analysis
        Linear regression
        Logarithmic regression
        Exponential regression
        Power regression

KEY INDEX

GENERAL KEYS

Key Function
[ON] ON
[0][9][.] Data entry
[+][-][x][/][=] Basic calculation
[AC] All clear
[C] Clear
[back] Backspace
[+/-] Sign change

MEMORY KEYS

Key Function
[MR] Independent memory recall
[Min] Independent memory in
[M+] Memory plus
[M-] Memory minus
[Kout] Constant memory recall
[Kin] Constant memory in

SPECIAL KEYS

Key Function
Shift
Mode
Parentheses
Exponent
Pi
Sexagesimal notation/decimal notation conversion
Register exchange
Register exchange
Rounding off internal value

FUNCTION KEYS

Key Function
Sine
Cosine
Tangent
Arc sine
Arc cosine
Arc tangent
Hyperbolic
Common logarithm
Common antilogarithm
Natural logarithm
Natural antilogarithm
Square root
Square
Engineering
Fraction
Cube root
Reciprocal
Factorial
Power
Root
Rectangular to polar
Polar to rectangular
Percent
Random number
Permutation
Combination

STATISTICAL KEYS

Key Function
Statistical register clear
Data entry
Data delete
Regression analysis data entry
Sample standard deviation
Population standard deviation
Arithmetic mean
Number of data
Sum of value
Sum of square value
Sum of value product
Constant term
Regression coeffizient
Correlations coeffizient
Estimator

1 / GENERAL GUIDE

1-1 Modes

To put the calculator into a desired operating mode or to select a specific angular unit, press [Mode]first then , ... or .
 
COMP mode. Carry out ordinary arithmetic and functional calculations.
LR is displayed. Calculate regression analysis.
SD is displayed. Calculate standard deviation.
DEG is displayed. Use degrees as the unit of angle measurement.
RAD is displayed. Use radians as the unit of angle measurement.
GRA is displayed. Use grads as the unit of angle measurement.
[Mode][7] Press any number from 0 to 7 to indicate how many decimal places you want displayed (FIX is displayed).
Press any number from 1 (1 digit) to 8 (8 digits) to indicate how many significant digits you want displayed (SCI is displayed).
Releases instructions entered in [Mode][7]and . This operation also changes the range of the exponent display.

1-2 The display

The display shows input data, interim results and answers to calculations. The mantissa section displays up to 8 digits. The exponent section displays up to ±99.
 
or  Error indication.
Pressing of .
Pressing of .
Something is being stored in the Memory.
A constant is being used in calculations.
Pressing of .
Standard deviation calculation.
Regression analysis calculation.
or  Angular unit.
Decimal places of a displayed value is being designated
Significant digits of a displayed value is being designated.
45-12/23
12°3'45,6"

Exponential Displays

The display can show calculation results only up to 8 digits long. When an intermediate value or a final result is longer, the calculator automatically switches over to exponential notation. Values greater than 99,999,999 are always displayed exponentially, while the lower limit is selectable. Note the following:
 
Type Lower limit Upper limit
A (Norm 1) 0.01 99,999,999
B (Norm 2) 0.0000001 99,999,999

Values less than the lower limits or greater than the upper limit shown above are displayed using exponential format. Use the following procedure to switch between the Type A lower limit and the Type B lower limit:

  1. Check the display to see if the FIX or SCI symbols are shown, indicating that the number of significant digits or the number of decimal places have been specified. If either of the symbols is shown, press to cancel the specification.
  2. Perform the following calculation: 1 200 
  3. Look at the display to see what the current lower limit is.

  4.   
    If the display reads:
    5.-03, the current setting is Type A
                        5. -03
    If the display reads:
    0.005, the current setting is Type B
    0.005 
  5. Press to switch between the Type A and Type B lower limits.
* Note that the lower limit is not changed if you press while the number of significant digits (SCI displayed) and/or the number of decimal places (FIX displayed) are specified. The first time you press  you clear the FIX and SCI specifications, and so you must press again to change the lower limit.

2 / ORDER OF OPERATIONS AND LEVELS

Operations are performed in the following order of precedence:
  1. Functions
  2. x y, x1/y, R->P, P->R, nPr, nCr
  3. x, 
  4. +, -
Operations with the same precedence are performed from left to right, with operations enclosed in parentheses performed first. If parentheses are nested, the operations enclosed in the innermost set of parentheses are performed first.

* Registers L1 through L6 are provided to store operations of lower precedence (including parenthetical operations). Since six registers are provided, calculations up to six levels can be retained.
* Since each level can contain up to three open parentheses, parantheses can be nested up to 18 times.

Example (4 levels, 5 nested parentheses)

Operation

Register contents at point A:
 
x 4
L1 [(  [(  5  +
L2 4 x 
L3 [(  [(  [(  3 +
L4 2 x
L5  
L6  

3 / CALCULATION RANGE AND SCIENTIFIC NOTATION

 
             
-9,9999999x1099
-107 -1 -10-2
-10-99 0 10-99
10-2 1 107
9,9999999x1099
  Normal display
  Scientific notation

When the answer exceeds the normal display capacity, it is automatically shown by scientific notation, 8-digit mantissa and exponents of 10 up to ±99.

1 The minus (-) sign for mantissa
2 The mantissa
3 The minus (-) sign for exponent
4 The exponent of ten
The whole display is read: - 1,2345678 x 10-99

* Entry can be made in scientific notation by using the key after entering the mantissa.
Example: -1.2345678 x 10-3 (= -0.0012345678)
 
OPERATION READ-OUT
2 3 4 5 6 7 8 
-1.2345678 
-1.2345678  00
-1.2345678 -03

4 / CORRECTIONS

If you notice an input mistake before you press the arithmetic operation key, simply press to clear the value and enter it again.
In a series of calculations, you can correct errors in intermediate results by recalculating correctly when the error appears and then continuing with the original series from where you interrupted it.
You can also use the key to backspace through an entered value until you reach the digit you wish to change and then make any necessary corrections. For example:

To change entry of 123 to 124:
 
OPERATION READ-OUT
123
123. 
12. 
4
124. 

If you make a mistake by pressing the wrong key when entering or simply press the appropriate key to correct. In this case, the most recently pressed key operation is used, but it retains the order of precedence of the original operation entered.

5 / OVERFLOW OR ERROR CHECK

Overflow or error is indicated by the "-E-" or "-[-" sign and stops further calculation

Overflow or error occurs:
a) When an answer, whether intermediate or final, or accumulated total in the memory is more than 1 x 10100 ("-E-" sign appears).
b) When function calculations are performed with a number exceeding the input range ("-E-" sign appears).
c) When unreasonable operations are performed in statistical calculations ("-E-" sign appears).
d) When the total number of levels of explicity and/or implicity (with addition-subtraction versus multiplication-division including x y und x1/y) nested parentheses exceeds 6, or more than 18 pairs of parentheses are used ("-[-" sign appears).

Ex.) You have pressed the key 18 times continously before designating the sequence .

To release these overflow checks:
a), b), c) Press the key.
d) Press the key. Or press the key, and the intermediate result just before the overflow occurs is displayed and the subsequent calculation is possible.

Memory protection:
The content of the memory is protected against overflow or error and the accumulated total is recalled pressing the key after the overflow check is released by the key.

6 / POWER SOURCE


The CASIO C-POWER system makes it possible to operate calculators any place even in complete darkness, you don't have to worry about the light conditions.


* This unit protects memory no matter what the light conditions.
* This unit uses two power sources: an amorphous silicon solar cell, and a lithium battery (GR927).
* A weakened lithium battery is indicated when memory contents spontaneously clear or when display darkens under poor light conditions and cannot be restored by pressing the key. Anytime such symptoms occur, the unit should be taken to your retailer or nearby dealer for battery replacement.
* Lithium battery replacement should only be performed by your retailer or an authorized dealer.
* To ensure proper operation the lithium battery should be replaced once every six years no matter how much the unit is used.

Auto power-off function
This unit automatically switches OFF if not operated for approximately 6 minutes. Power can be restored by pressing the key. Memory contents and mode setting are retained even when power is switched off.

7 / SPECIFICATIONS

BASIC OPERATIONS

4 basic calculations, constants for + / - / x  / / xy,x1/y, parenthesis calculations and memory calculations.

BUILT-IN FUNCTIONS

Trigonometric/inverse trigonometric functions (with angle in degrees, radians or grads), hyperbolic/inverse hyperbolic functions, common/natural logarithms, exponential functions (common antilogarithms, natural antilogarithms), powers, roots, square roots, cube roots, squares, reciprocals, factorials, conversion of coordinate system (R->P, P->R), permutations, combinations, random number, pi, fractions, percentages and logical operations.

STATISTICAL FUNCTIONS

Standard deviation, linear regression, logarithmic regression, exponential regression, and power regression.

MEMORY

1 independent memory and 6 constant memories.

CAPACITY

Entry/basic calculations

8-digit mantissa, or 8-digit mantissa plus 2-digit exponent up to 10±99

Fraction calculations

Total of integer, numerator and denominator must be within 8 digits (includes division marks).
 
Scientific functions Input range
sinx/cosx/tanx |x| < 9 x 109 degrees
|x| < 5 x 107 rad
|x| < 1010 gra
sin-1x/cos-1x |x| <= 1
tan-1x |x| < 10100
sinhx/coshx |x| <= 230,2585
tanhx |x| < 10100
sinh-1x |x| < 5 x 1099
cosh-1x 1 <= x < 5 x 1099
tanh-1x |x| < 1
logx/lnx 10-99 <= x <= 10100
ex -10100 < x <= 230,2585
10x -10100 < x < 100
x y x > 0: -10100 < y logx < 100
x = 0: y > 0
x < 0: y: integer or 1/2n+1 (n integer)
x1/y x > 0: y 0 -10100 < 1/y logx < 100
x = 0: y > 0
x < 0: y: odd number or 1/n (n integer)
0 <= x < 10100
x2 |x| <  1050
|x| <  10100
1/x |x| <  10100 (x 0)
x! 0 <= x <= 69 (x: integer)
nPr / nCr 0 <= 0 r <= n, n < 1010 (n, r: integer)
* Certain combinations or permutations may cause errors due to overflow during internal calculations.
REC -> POL < 10100
POL -> REC |x| < 9 x 109 degrees
|x| < 5 x 107 rad
|x| < 1010 gra
0 <= r <= 10100
° ' " up to second
8 digits

* Errors are cumulative with such internal continous calculations as xy,x1/yx!so accuracy rnay be adversely affected.

* Output accuracy
± 1 in the 8th digit.

DECIMAL POINT

Full floating with underflow.

EXPONENTIAL DISPLAY

Norm 1 - 10-2 > |x|,    |x| >= 108
Norm 2 - 10-7 > |x|,    |x| >= 108

READ-OUT

Liquid crystal display, suppressing unnecessary O's (zeros).

POWER SOURCE

Power source: Amorphous silicon solar cell, lithium battery (GR927)
Lithium battery life: 6 years with GR927 (1-hour daily use).

AMBIENT TEMPERATURE RANGE

O °C bis 40 °C (32 °F - 104 °F)

DIMENSIONS

17.5mmH x 73mmW x 140mmD
(3/4"H x 27/8"W x 51/2"D) - fx-85V
8.5mmH x 73mmW x 140mmD
(5/16"H x 27/8"W x 51/2"D) - fx-911V

WEIGHT

64 g (2.3 oz) - fx-85V
59 g (2.1 oz) - fx-911V

8 / NORMAL CALCULATIONS

* You can perform normal calculations in the COMP mode ().
* Calculations can be performed in the same sequence as the written formula (true algebraic logic).
* Nesting of up to 18 parentheses at 6 levels is allowed.

8-1 Four basic calculations (incl. parenthesis calculations)

        EXAMPLE         OPERATION READ-OUT
23 + 4.5 -53 =
23 53 
-25.5 

56 x (-12) (-2.5) =

56 12 [+/-]
268.8 

3 x (1 x 1020) =

20 
6.6666667  19

7 x 8 - 4 x 5 (= 56 - 20 ) =

36. 

1 + 2 - 3 x 4 5 + 6 = 

6.6

 
6

 4 x 5
 =

0.3


* The number of levels of the key can be displayed.
 
2 x { 7 + 6 x (5 + 4) } =
[01                    0.
[02                    0.
122.


* It is unnecessary to press the key before the key.
 
10 - { 7 x (3 + 6 ) } = 
10 
-53. 

Another operation: 10 36


8-2 Constant calculations

* The "K" sign appears when a number is set as a constant..
 
3 + 2.3 =
                              5.3
6 + 2.3 =
                              8.3



 
2.3 x 12 = 12 
                             27.6
(-9) x 12 =
                           -108.



 
17 + 17 + 17 + 17 =
17 
                              34.
                              51.
                              68.



 
1.72 = 1.7 
                           2.89
1.73 =
                         4.913
1.74 =
                       8.3521



 
3 x 6 x 4 =
                             18.
3 x 6 x (-5) =
                             72.

                           -90.



 
56

4 x (2 + 3)
 =  23

4 x (2 + 3)
 =

                              20.
56 
                              2.8
23 
                            1.15


8-3 Memory calculations using the independent memory

* When a new number is entered into the independent memory by the key, the previous number stored  is automatically cleared and the new number is put in the independent memory.
* The "M" sign appears when a number is stored in the memory .
* The contents accumulated into the independent memory are preserved even after the power switch is tuned off.
To clear the contents press [0]or [AC]in sequence.

       53 + 6 =   59
       23 -  8 =  15
       56 x  2 = 112
+ )   994 =    24.75


                      210.75
 
53 
                                 59.
23 
                                 15.
56 
                               112.
99 
                             24.75
                           210.75



 
7 + 7 - 7 + (2 x 3) + (2 x 3) + (2 x 3) - (2 x 3) =
                                 19.



        12 x 3 =   36
- )    45 x 3 =  135
        78 x 3 =  234

                      135
 
12 
                             36.
45 
                           135.
78 
                           234.
                           135.


8-4 Memory calculations using 6 constant memories

* When a new number is entered into a constant memory by operating ENTRY (to ), the previous number stored is automatically cleared and the new number is put in the constant memory.
* The contents stored in the constant memories are preserved even after the power switch is turned off. To clear the contents press (to ) or (to ) in sequence.
 
 
193.2 23 =
193 23 
8.4
193.2 28 =
28 
6.9
193.2 42 =
142
4.6

* Another operation by using the independent memory:
193 23 28 42 



 
9 x 6 + 3

(7 - 2) x 8
=

 57.
40.
1.425


* Calculations in constant memory registers can also be performed by using the and keys:

  7  x  8  x  9  =  504
  4  x  5  x  6  =  120
  3  x  6  x  9  =  162



14     19    24     786    (Total)
 
 
8
                               504.
                               120.
                               162.
                                 14.
                                 19.
                                 24.
                               786.



 
12 x (2.3 + 3.4) - 5 =
30 x (2.3 + 3.4 + 4.5) - 15 x 4.5

12 
 63.4
 30 15 
238.5

The keys are pressed to exchange the displayed number (4.5) with the contents of constant memory 1.


8-5 Fraction calculations

* Total of integer, numerator and denominator must be within 8 digits (includes division marks).
* A fraction can be transferred to the memory.
* When a fraction is extracted, the answer is displayed as a decimal.
* A press of key after the converts the fraction answer to the decimal scale.
 
 
4 5
6
 x (3 1
4
 + 1 2
3
7 8
9
=
 3_7_568.
3.0123239
3_7_568.



 
2 4
5
 +  3
4
 - 1 1
2
=
 3_11_20.
3.55
2_1_20.



 
(1.5 x 107) - {(2.5 x 106) x 3

100
} =
1.5 100 
14925000.


* During a fraction calculation, a figure is reduced to the lowest terms by pressing a function command key (,oder) or the if the figure is reducible:
 
3 456
78
 =  8 11
13
 (Reduction)
456 78
 3_456_78.
8_11_13.

* By pressing continuously, the displayed value will be converted to the improper fraction.
Continuing from above:
 
 115_13.



 
12
45
- 32
56
 =
12 45 
 4_15.
32 56 
-32_105.


* The answer in a calculation performed between a fraction and a decimal is displayed as a decimal:
 
41
52
 x 78.9 =
41 52 
 41_52.
78 
62.209615


8-6 Percentage calculations

12% of 1500:
1500 12 
 180.


Percentage of 660 against 880:
660 880 
 75.


15% add-on of 2500:
2500 15 
 2875.


25% discount of 3500:
3500 25 
 2625.


300cc is added to a solution of 500cc. What is the percent of the new volume to the initial one?
300 500 
 160.
(%)


If you made $80 last week and $100 this week, what is the percent increase?
100 80 
 25.
(%)


12% of 1200:
18% of 1200:
23% of 1200:
1200 12 
                             144.
18 
                             216.
23 
                             276.


26% of 2200:
26% of 3300:
26% of 3800:
26 2200 
                             572.
3300 
                             858.
3800 
                             988.


Percentage of 30 against 192?:
Percentage of 156 against 192?:
192 30
                          15.625
156 
                            81.25


* 600 grams was added to 1200 grams. What percent is the total to the initial weight?
* 510 grams was added to 1200 grams. What percent is the total to the initial weight?
1200 600 
                              150.
510 
                            142.5


* How many percent down is 138 grams to 150 grams?
* How many percent down is 129 grams to 150 grams?
150 138 
                                -8.
129 
                              -14.


9 / FUNCTION CALCULATIONS

Scientific function keys can be utilized as subroutines of four basic calculations (including parentheses calculations).
* This calculator computes as = 3,1415927 und e= 2,7182818.
* In some scientific functions, the display disappears mometarily while complicated fomulas are being processed. So do not enter numerals or press the function key until the previous answer is displayed.
* For each input range of the scientific functions, see the specifications.

9-1 Sexagesimal <-> Decimal conversion

The key converts the sexagesimal figure (degree, minute and second) to decimal notation. Operation of converts the decimal notation to the sexagesimal notation.

14°25'36" =
14 
14.
25 
14.416667.
36 
14.426667.
14°25°36.


9-2 Trigonometric/Inverse trigonometric functions

sin (   
6
rad) =
"RAD" ()
 0.5


cos 63°52'41" =
"DEG" () 63 52 41
 63.878056
0.440283


tan (-35 gra) =
"GRA" () 35 
 -0.6128007


2 x sin 45° x cos 65° =
"DEG" 2 45 65
 0.5976724



 
cot 30°  =  1

tan 30°
 =
"DEG" 30 
 1.7320508



 
sec (   
3
rad) =


1

cos ( 
3
 rad)
 =
"RAD" 
 2.



 
cosec 30°  =  1

sin 30°
 =
"DEG" 30 
 2.



 
cos-1   
2
 =
"RAD" 2 
 0.7853981


tan-1 (0.6104) =
"DEG" 6104 
 31.399891
31°23°59.

9-3 Hyperbolic functions and inverse hyperbolic functions

sinh 3.6 =
 18.285455


tanh 2.5 =
 0.9866143


cosh 1.5 - sinh 1.5 =
                      2.3524096
                        0.223130
                                -1.5


sinh-1 30 =
30 
 4.0946222


Solve tanh (4x) = 0.88:
 
x
tanh-1 0.88

4
 =
88 
 0.3439419


9-4 Common & Natural logarithms/ Exponentiations (Common antilogarithms, Natural antilogarithms, Powers and Roots)

log 1.23 (= log101.23) =
23
 0.0899051


Solve 4x = 64:
x log 4 = log 64
x log 64
log 4
64 4
 3.


ln 90 (= loge 90) =
90 
4.4998097


log 456 ln 456 =
456 
0.4342944


100.4 + 5 e-3 =
2.7608218


5.62.3  =
52.581438


1231/7 (= )  =
123 
1.9886478


(78 - 23)-12 =
78 23 12 
1.3051118 - 21


312 + e10 =
 3 12 10 
553467.47


log sin 40° + log cos 35° =
"DEG" 40 35 
 -0.2785679
0.5265407
(The Antilogarithm................................0.5265407)


9-5 Square roots, Cube roots, Squares, Reciprocals & Factorials

=
 2 
5.2871969

=
 5 27 
-1.2900241


123 + 302 =
 123 30 
1023.



 
 
1

 =
1

3
 -  1

4

 3 
12.


8! (= 1 x 2 x 3 x ..... x 7 x 8) =
 8 
40320.


9-6 Miscellaneous functions (FIX, SCI, NORM, RND, RAN#, ENG)

1.234 + 1.234 =
"FIX2" ()
 1 234 

1.23
234 

2.47

2.468
1.234 + 1.234 =
"FIX2"
234 

1.23
234 

2.46

2.46


3 + 1 3 =
"SCI2" ()

3.3 -01

6.7 -01

0.6666666
3 + 1 3 =
"SCI2"

3.3 -01

6.6 -01

0.66


1000 = 0.001
              = 1 x 10-3
(Norm 1)   1 1000
3. -03
(Norm 2) 
0.001


123 m x 456 = 56088 m = 56.088 km
123 456
56088
56.088  03


7.8 g96 = 0.08125 g = 81.25 mg
96 
0.08125
81.25 -03


Generate a random number between 0.000 and 0.999.
0.570
(Example)


9-7 Polar to rectangular co-ordinates conversion

  Formula: x= rcos ßy=rsinß

Ex.)
Find the value of x and y when the point P is shown as ß = 60° and length r = 2 in the polar co-ordinates:
"DEG"
60 
1.
(x)
1.7320508
(y)


9-8 Rectangular to polar co-ordinates conversion

Formula: r, ß= tan-1(y/x) (-180°<ß<= 180°)

Ex.)
Find the length r and angle ß in radian when the point P is shown as x = 1 und yin the rectangular co-ordinate:
"RAD"
2.
(r)
1.0471976
(ß in radian)


9-9 Permutations

Input range: n>= r(n, r: natural Numbers)
Formula:            nPr n!

(n - r)!

Ex.)
How many numbers of 4 figures can be obtained when permuting 4 different numbers among 7 (1 to 7)?
840.


9-10 Combinations

Input range: n>= r(n, r: natural Numbers)
Formula:            nCr n!

r! (n - r)!

Ex.)
How many groups of 4 members can be obtained when there are ten in class?
10 
210.


10 / STATISTICAL CALCULATIONS

* Be sure to press in sequence prior to starting a statistical calculation.

10-1 Standard deviation

* Set the function mode to "SD" by pressing .
Ex.)
Find , n, and based on the data 55, 54, 51, 55, 53, 53, 54, 52.
"SD"
55 54 51 55 53 53 54 52 
52.
(Sample standard deviation)
1.407886
(Population standard deviation)
1.3169567
(Arithmetical mean)
53.375
(Number of data)
8.
(Sum of value)
427.
(Sum of square value)
22805.
Calculate the unbiased variance and the deviation between each data item and the average.
(Subsequently)
  1.9821429
(Unbiased variance)
55 
1.625
(55 - )
54 
0.625
(54 - )
51
-2.375
(51 - )



.
.
.
.
.
Note:
The sample standard deviation is defined as:

The population standard deviation is defined as:

and the arithmetical mean is defined as:

* Pressing or key need not be done sequentially.

Ex.)
Find nund , based on the data: 1.2, -0.9, -1.5, 2.7, -0.6, 0.5, 0.5, 0.5, 0.5, 1.3, 1.3, 1.3, 0.8, 0.8, 0.8, 0.8, 0.8.
"SD"
-0.9
1) (Mistake)
-2.5
1') (To  correct)
0.
-1.5
2.7
2) (Mistake)
2.7
3) (Mistake)
-1.6
3') (To  correct)
-1.6
-0.6
2') (To  correct)
2.7
0.5
0.5
4) (Mistake)
1.4
4') (To  correct)
0.
1.3
0.8
5) (Mistake)
0.8
5') (To  correct)
0.8
0.8
17.
0.6352941
0.9539006

10-2 Regression analysis

Set the function mode to "LR" by pressing .

Linear regression

Formula:

Ex.)
Results from measuring the length and temperature of a steel bar.
 
temp./°C length/mm
10
15
20
25
30
1003
1005
1010
1008
1014

Find the constant term (A), regression coefficient (B), correlation coefficient (r) and estimated values () using the above figures as a basis.
 
10 
10.
1003 
1003.
15 1005 
1005.
20 1010 
1010.
25 1008 
1008.
30 1014 
1014.
998.
(A)
0.5
(B)
0.9190182
(r)
(When the temp. is 18 °C)
18 
1007.
(mm)
(When the length is 1000 mm)
1000 
4.
(°C)
Note:
, n, A, B and r are respectively obtained by pressing a numeral key (to ) after the - or -key.

* Correction of data entry
Ex.)
 
xi 2 3 2 3 2 4
yi 3 4 4 5 5 5

"LR"
3.
1) (Mistake)
4
4.
1') (To correct)
0.
3.
4.
2) (Mistake)
3.
2') (To correct)
2.
4.
3) (Mistake)
1.
5.
3') (To correct)
5.
5.
4.
4) (Mistake)
4.
4.
5) (Mistake)
6.
5') (To correct)
6.
5.
4') (To correct)
 2 
4.
5.

These ways of correction can also be applied to logarithmic, exponential or power regression.

Logarithmic regression

Formula: 

* Input data items are the logarithm of x (ln x), and y which is the same as in linear regression.
* Operation for calculating and correcting regression coefficients are basically the same as in linear regression. Operate the sequence x to obtain estimator and y for estimator .
Note that and are obtained instead of and respectively.

Ex.)
 
xi 29 50 74 103 118
yi 1.6 23.5 38.0 46.4 48.9

Find Sie A, B, r, and using the above figures as a basis..
"LR"
29 
3.3672958
1.6
50 23 
1005.
74 38 
38.
103 46 
46.4
118 48 
48.9
-111.1284
(A)
34.020147
(B)
0.9940139
(r)
(When xi is 80)
80 
37.948795
()
(When yi is 73)
73 
224.15413
()

Exponential regression

Formula: 

* Input data items are the logarithm of y (ln y), and x which is the same as in linear regression.
* Operation for correction is basically the same as in linear regression. Operate to obtain coefficient A, x for estimator , and y for estimator .
Note that and are obtained instead of and .

Ex.)
 
xi 6.9 12.9 19.8 26.7 35.1
yi 21.4 15.7 12.1 8.5 5.2

Find A, B, r, and using the above figures as a basis.
"LR"
6
6.9
21 
3.0633909
12 15 
2.7536607
1912 
2.4932055
26 
2.1400662
35 1
1.6486586
30.497587
(A)
-0.0492037
(B)
-0.9972473
(r)
(When xi is16)
16 
13.879157
()
(When yi is 20)
20 
8.574868
()

Power regression

Formula: 

*  Input data items are lnx und lny.
* Operation for correcting is basically the same as in linear regression. Operate   to obtain coefficient A, x for estimator and y for estimator . Note that and are obtained instead of and respectively.

Ex.)
 
xi 28 30 33 35 38
yi 2410 3033 3895 4491 5717

Find A, B, r, und using the above figures as a basis.
"LR"
28 
3.3322045
2410 
7.787382
30 3033
8.0173075
33 3895 
8.267449
35 4491 
8.4098307
38 5717 
8.6511995
0.238801
(A)
2.7718661
(B)
0.9989062
(r)
(When xi is 40)
40 
6587.6748
()
(When yi is 1000)
1000 
20.262257
()