Casio fx-82AR X User manual

EN
http://edu.casio.com
User’s Guide
CASIO Worldwide Education Website
http://world.casio.com/manual/calc
Manuals are available in multi languages at
Be sure to keep all user documentation handy for future reference.
fx-95AR X
fx-82AR X

CONTENTS
About this Manual......................................................................................2
Initializing the Calculator........................................................................... 2
Precautions................................................................................................2
Getting Started.......................................................................................... 3
Calculation Mode.......................................................................................4
Input and Output Formats......................................................................... 5
Configuring the Calculator Setup.............................................................. 6
Inputting Expressions and Values............................................................. 7
Toggling Calculation Results..................................................................... 9
Basic Calculations................................................................................... 10
Calculation History and Replay............................................................... 11
Using Memory Functions.........................................................................11
Function Calculations.............................................................................. 12
Statistical Calculations.............................................................................15
Equation Calculations (fx-95AR X only)...................................................17
Creating a Number Table........................................................................ 19
Inequality Calculations (fx-95AR X only)................................................. 20
Ratio Calculations (fx-95AR X only).........................................................20
Errors....................................................................................................... 21
Before Assuming Malfunction of the Calculator... .................................22
Replacing the Battery.............................................................................. 22
Technical Information...............................................................................22
■■ Frequently Asked Questions ■■.........................................................25
• In no event shall CASIO Computer Co., Ltd. be liable to anyone for
special, collateral, incidental, or consequential damages in connection
with or arising out of the purchase or use of this product and items that
come with it.
• Moreover, CASIO Computer Co., Ltd. shall not be liable for any claim of
any kind whatsoever by any other party arising out of the use of this
product and the items that come with it.
1

About this Manual
• Unless specifically stated, all sample operations in this manual assume
that the calculator is in its initial default setup. Use the procedure under
“Initializing the Calculator” to return the calculator to its initial default
setup.
• The contents of this manual are subject to change without notice.
• The displays and illustrations (such as key markings) shown in this User’s
Guide are for illustrative purposes only, and may differ somewhat from
the actual items they represent.
• Company and product names used in this manual may be registered
trademarks or trademarks of their respective owners.
Initializing the Calculator
Perform the following procedure when you want to initialize the calculator
and return the calculation mode and setup (except Language and Contrast
settings) to their initial default settings. Note that this operation also clears
all data currently in calculator memory.
(RESET)(Initialize All)(Yes)
Precautions
Safety Precautions
Battery
• Keep batteries out of the reach of small children.
• Use only the type of battery specified for this calculator in this manual.
Handling Precautions
• Even if the calculator is operating normally, replace the battery at least
once every two years. A dead battery can leak, causing damage to and
malfunction of the calculator.
• The battery that comes with the calculator discharges slightly during
shipment and storage. Because of this, it may require replacement
sooner than the normal expected battery life.
• Avoid use and storage of the calculator in areas subjected to
temperature extremes, and large amounts of humidity and dust.
• Do not subject the calculator to excessive impact, pressure, or bending.
• Never try to take the calculator apart.
• Use a soft, dry cloth to clean the exterior of the calculator.
• Whenever discarding the calculator or batteries, be sure to do so in
accordance with the laws and regulations in your particular area.
2

Getting Started
Before using the calculator, slide its hard case
downwards to remove it, and then affix the hard
case to the back of the calculator as shown in the
illustration nearby.
Turning Power On and Off
Press to turn on the calculator. Press
(OFF) to turn off the calculator.
Note: The calculator also will turn off automatically after approximately 10
minutes of non-use. Press the key to turn the calculator back on.
Adjusting Display Contrast
Display the Contrast screen by performing the key operation below:
(SETUP)*1or *2(Contrast). Next, use and to
adjust contrast. After the setting is the way you want, press .
*1: fx-82AR X *2: fx-95AR X
Important: If adjusting display contrast does not improve display
readability, it probably means that battery power is low. Replace the battery.
Key Markings
Pressing the or key followed by a second key
performs the alternate function of the second key. The alternate
function is indicated by the text printed above the key.
(1) Keycap function (2) Alternate function
This color: Means this:
Yellow Press and then the key to access the
applicable function.
Red
Press and then the key to input the
applicable variable, constant, function, or
symbol.
Reading the Display
• If a or indicator appears on the right side of either the input
expression line or calculation result line, it means the displayed line
continues to the right. Use and to scroll the line display. Note that
if you want to scroll the input expression while both the and 
indicators are displayed, you will need to press first and then use 
and to scroll.
• The table below describes some of the typical indicators that appear at
the top of the screen.
3

The keypad has been shifted by pressing the key. The
keypad will unshift and this indicator will disappear when you
press a key.
The alpha input mode has been entered by pressing the 
key. The alpha input mode will be exited and this indicator
will disappear when you press a key.
//Indicates the current setting of Angle Unit (: Degree, :
Radian, or : Gradian) on the setup menu.
FIX A fixed number of decimal places is in effect.
SCI A fixed number of significant digits is in effect.
MThere is a value stored in independent memory.

The calculator is standing by for input of a variable name to
assign a value to the variable. This indicator appears after
you press .
Indicates that MathI/MathO or MathI/DecimalO is selected for
Input/Output on the setup menu.
The display currently shows an intermediate result of a multi-
statement calculation.
Using Menus
Some of the operations of this calculator are performed using menus.
Menus are displayed by pressing or and then (SETUP).
General menu operation operations are described below.
• You can select a menu item by pressing the number key that
corresponds to the number to its right*1or left*2on the menu screen.
or
*1*2
• A vertical scroll bar (1) indicates that the menu runs off the screen. In this
case, you can use and to scroll the menu up and down. A right*1
or left*2arrow (2) indicates that the currently displayed menu is a sub-
menu. To return from a sub-menu to its parent menu, press *1or
*2.
• To close a menu without selecting anything, press .
*1 Language: Arabic *2 Language: English
Calculation Mode
Specify the calculation mode that is suitable for the type of calculation you
want to perform.
1. Press  to display the Main Menu.
2. Use the cursor keys to move the
highlighting to the icon you want.
(Example: fx-95AR X)
For this: Select this icon:
4

General calculations (Calculate)
Statistical and regression calculations (Statistics)
Generate a number table based on one
or two functions (Table)
Equation and function calculations (Equation/Func)*
Inequality calculations (Inequality)*
Ratio calculations (Ratio)*
* fx-95AR X only
3. Press to display the initial screen of the mode whose icon you
selected.
Note: The initial default calculation mode is the Calculate Mode.
Input and Output Formats
Before starting a calculation on the calculator, you should first use the
operations in the table below to specify the formats that should be applied
for calculation formula input and calculation result output.
To specify this type of input and output:
Press (SETUP)


(Input/Output) and then
press:
Input: Natural Textbook; Output: Format that
includes a fraction, √, or π*1(MathI/MathO)
Input: Natural Textbook; Output: Converted
to decimal value (MathI/DecimalO)
Input: Linear*2; Output: Decimal or fraction (LineI/LineO)
Input: Linear*2; Output: Converted to
decimal value (LineI/DecimalO)
*1 Decimal output is applied when these formats cannot be output for
some reason.
*2 All calculations, including fractions and functions are input in a single
line. Same output format as that for models without Natural Textbook
Display (S-V.P.A.M. models, etc.)
Input/Output Format Display Examples
MathI/MathO
MathI/DecimalO
5

LineI/LineO
LineI/DecimalO
Note: The initial default input/output format setting is MathI/MathO.
Configuring the Calculator Setup
To change the calculator setup
1. Press (SETUP) to display the setup menu.
2. Use and to scroll the setup menu, and then input the number
displayed to the right*1 or left*2 of the item whose setting you want to
change.
*1 Language: Arabic *2 Language: English
Items and Available Setting Options
“◆” indicates the initial default setting.
Input/Output 

MathI/MathO◆;

MathI/DecimalO;

LineI/LineO;

LineI/DecimalO Specifies the format to be used by the calculator for
formula input and calculation result output.
Angle Unit

Degree◆;

Radian;

Gradian Specifies degree,
radian or gradian as the angle unit for value input and calculation result
display.
Number Format Specifies the number of digits for display of a calculation
result.

Fix: The value you specify (from 0 to 9) controls the number of decimal
places for displayed calculation results. Calculation results are rounded off
to the specified digit before being displayed.
Example: 1007(≈)* 14.286 (Fix 3)

Sci: The value you specify (from 0 to 9) controls the number of
significant digits for displayed calculation results. Calculation results are
rounded off to the specified digit before being displayed.
Example: 17(≈)* 1.4286 × 10-1 (Sci 5)

Norm: Displays calculation results in exponential format when they fall
within the ranges below.

Norm 1◆:10-2 > |x|, |x| ≧1010,

Norm 2: 10-9 > |x|, |x| ≧1010
Example: 1200(≈)* 5 × 10-3 (Norm 1), 0.005 (Norm 2)
* Pressing (≈) instead of after inputting a calculation will display
the calculation result in decimal form.
Fraction Result

ab/c;

d/c◆Specifies either mixed fraction or
improper fraction for display of fractions in calculation results.
Complex (fx-95AR X only)

a+bi◆;

r
∠
θSpecifies either rectangular
coordinates or polar coordinates for Equation/Func Mode solutions.
Note: An iindicator is displayed at the top of the screen while a+biis
selected for the Complex setting. ∠is displayed while r∠θis selected.
6

Statistics 

On;

Off◆Specifies whether or not to display a Freq
(frequency) column in the Statistics Mode Statistics Editor.
Equation/Func (fx-95AR X only)

On◆;

Off Specifies whether or not
to use complex numbers in solutions output in the Equation/Func Mode.
Table

f(x);

f(x),g(x)◆Specifies whether to use function f(x) only or
the two functions f(x) and g(x) in the Table Mode.
Decimal Mark

Dot◆;

Comma Specifies whether to display a dot or
a comma for the calculation result decimal mark. A dot is always displayed
during input.
Note: When dot is selected as the decimal mark, the separator for multiple
results is a comma (,). When comma is selected, the separator is a
semicolon (;).
Digit Separator

On;

Off◆Specifies whether or not a separator
character should be used in calculation results.
MultiLine Font

Normal Font◆;

Small Font Specifies the display
font size when LineI/LineO or LineI/DecimalO is selected for Input/Output.
Up to four lines can be displayed while Normal Font is selected, and up to
six lines can be displayed with Small Font.
Language

English;

Arabic◆Specifies the language to be used for
calculator menus and messages.
To initialize calculator settings (except the Contrast setting)
(RESET)(Setup Data)(Yes)
Inputting Expressions and Values
Basic Input Rules
When you press the priority sequence of the input calculation will be
evaluated automatically and the result will appear on the display.
4 × sin 30 × (30 + 10 × 3) = 120
*1 Input of the closing parenthesis is required for sin and other functions
that include parentheses.
*2 These multiplication symbols (×) can be omitted.
*3 The closing parenthesis immediately before the operation can be
omitted.
Note
• The cursor will change shape to when there are 10 bytes or less of
allowed input remaining. If this happens, end calculation input and then
press .
• If you execute a calculation that includes both division and multiplication
operations in which a multiplication sign has been omitted, parentheses
will be inserted automatically as shown in the examples below.
- When a multiplication sign is omitted immediately before an open
parenthesis or after a closed parenthesis.
Example: 6 ÷ 2 1 + 2 6 ÷ 21 + 2
- When a multiplication sign is omitted immediately before a variable, a
constant, etc.
Example: 2÷2 2 2 ÷ 2 2
7

Calculation Priority Sequence
The priority sequence of input calculations is evaluated in accordance with
the rules below. When the priority of two expressions is the same, the
calculation is performed from left to right.
1 Parenthetical expressions
2
Functions that have parentheses (sin(, log(, etc., functions that take
an argument to the right, functions that require a closing parenthesis
after the argument)
3Functions that come after the input value (𝑥2, 𝑥3, 𝑥-1, 𝑥!, °’ ”, °, r, g, %),
powers (), roots ( )
4 Fractions
5 Negative sign ((-))
6Statistics Mode estimated values (𝑥, 𝑦, 𝑥1, 𝑥2)
7 Multiplication where the multiplication sign is omitted
8Permutation (nPr), combination (nCr)
9 Multiplication (×), division (÷)
10 Addition (+), subtraction (−)
Note: When squaring a negative value (such as -2), the value being
squared must be enclosed in parentheses (2). Since x2has
a higher priority than the negative sign, inputting 2 would result in
the squaring of 2 and then appending a negative sign to the result. Always
keep the priority sequence in mind, and enclose negative values in
parentheses when required.
Inputting an Expression Using Natural Textbook
Format (MathI/MathO or MathI/DecimalO Only)
Formulas and expressions that include fractions and/or special functions
such as √can be input in natural textbook format by using templates that
appear when certain keys are pressed.
Example: 31
2+53 2
1. Press ().
• This inputs a mixed fraction template.
2. Input values into the integer, numerator, and denominator areas of the
template.
312
3. Do the same to input the remainder of the expression.
() 532
Tip: While the input cursor is located within the input area of a template
(mixed fractions), pressing  jumps to the position immediately
following (to the right) of the template, while pressing  jumps to the
position immediate before (to the left of) it.
8

Note
• When you press and obtain a calculation result, part of the
expression you input may be cut off. If you need to view the entire input
expression again, press and then use and to scroll the input
expression.
• Nesting of functions and parentheses is allowed. Further input will
become impossible if you nest too many functions and/or parentheses.
To undo operations (MathI/MathO or MathI/DecimalO only): To undo the
last key operation, press (UNDO). To redo a key operation you have
just undone, press (UNDO) again.
Using Values and Expressions as Arguments (MathI/
MathO or MathI/DecimalO only)
Example: To input 1+ 7
6and then change it to 1+ 7 6
176(INS)

Pressing (INS) in the above example causes 7
6to be the argument
of the function input by the next key operation (√).
Overwrite Input Mode (LineI/LineO or LineI/DecimalO
only)
In the overwrite mode, text you input replaces the text at the current cursor
location. You can toggle between the insert and overwrite modes by
performing the operations: (INS). The cursor appears as “” in the
insert mode and as “” in the overwrite mode.
Toggling Calculation Results
While MathI/MathO or MathI/DecimalO is selected for Input/Output on the
setup menu, each press of will toggle the currently displayed
calculation result between its fraction form and decimal form, its √form
and decimal form, or its πform and decimal form.
𝜋÷6= 1
6𝜋=0.5235987756 (MathI/MathO)
(π)61
6π←→0.5235987756
2+2 ×3=5.913591358 = 6+2 3 (MathI/DecimalO)
2235.913591358 ←→6+2 3
Regardless of what is selected for Input/Output on the setup menu, each
press of will toggle the currently displayed calculation result between its
decimal form and fraction form.
Important
• With certain calculation results, pressing the  key will not convert the
displayed value.
9

• You cannot switch from decimal form to mixed fraction form if the total
number of digits used in the mixed fraction (including integer, numerator,
denominator, and separator symbol) is greater than 10.
To obtain a decimal value calculation result while MathI/MathO or LineI/
LineO is selected
Press (≈) instead of after inputting a calculation.
Basic Calculations
Fraction Calculations
Note that the input method for fractions depends on the current Input/
Output setting on the setup menu.
2
3+11 2=13 6(MathI/MathO) 23()
112
13
6
(LineI/LineO) 23112136
Note
• Mixing fractions and decimal values in a calculation while something
other than MathI/MathO is selected will cause the result to be displayed
as a decimal value.
• Fractions in calculation results are displayed after being reduced to their
lowest terms.
• To switch a calculation result between improper fraction and mixed
fraction form, press ().
Percent Calculations
Inputting a value and pressing (%) causes the input value to
become a percent.
150 × 20% = 30 15020(%)30
Calculate what percentage of 880 is 660. (75%)
660880(%)75
Discount 3500 by 25%. (2625)
3500350025(%)2625
Degree, Minute, Second (Sexagesimal) Calculations
The syntax below is for inputting a sexagesimal value: {degrees} 
{minutes}  {seconds} . Note that you must always input something
for the degrees and minutes, even if they are zero.
2°20’30” + 9’30” = 2°30’00”
220300930 2°30’0”
Convert 2°30’0” to its decimal equivalent. 2.5
(Converts decimal to sexagesimal.) 2°30’0”
Multi-Statements
You can use the colon character (:) to connect two or more expressions and
execute them in sequence from left to right when you press .
3 + 3 : 3 × 3 33(:) 336
9
Note: Inputting a colon (:) while LineI/LineO or LineI/DecimalO is selected
for the Input/Output setting on the setup menu causes a newline operation
to be performed.
10

Using Engineering Notation
Transform the value 1234 to engineering
notation, shifting the decimal mark to the
right, and then to the left.
12341234
1.234×103
1234×100
(←)1.234×103
(←)0.001234×106
Prime Factorization
In the Calculate Mode, a positive integer no more than 10 digits long can be
factored to prime factors.
To perform prime factorization on 1014
10141014
(FACT) 2×3×132
To re-display the unfactored value, press (FACT) or .
Note: The types of values described below cannot be factored, even if they
have 10 or fewer digits.
• One of the prime factors of the value is 1018081 or greater.
• Two or more of the prime factors of the value have more than three digits.
The part that cannot be factored will be enclosed in parentheses on the
display.
Calculation History and Replay
Calculation History
An and/or at the top of the display indicates that there is more
calculation history content above and/or below. You can scroll through
calculation history contents using and .
2 + 2 = 4 224
3 + 3 = 6 336
(Scrolls back.) 4
Note: Calculation history data is all cleared whenever you press , when
you change to a different calculation mode, when you change the Input/
Output setting, or whenever you perform a RESET operation (“Initialize All”
or “Setup Data”).
Replay
While a calculation result is on the display, you can press or to edit
the expression you used for the previous calculation.
4 × 3 + 2 = 14 43214
4 × 3 − 7 = 5 (Continuing) 75
Using Memory Functions
Answer Memory (Ans)
The last calculation result obtained is stored in Ans (answer) memory.
To divide the result of 14 × 13 by 7
1413182
(Continuing) 7
11

123 + 456 = 579
789 − 579 = 210
123456
(Continuing) 789
579
210
Variables (A, B, C, D, E, F, M, x, y)
You can assign values to variables and use the variables in calculations.
To assign the result of 3 + 5 to variable A
35(A) 8
To multiply the contents of variable A by 10
(Continuing) (A)10*180
To recall the contents of variable A
(Continuing) (RECALL)*2
(A)8
To clear the contents of variable A
0(A) 0
*1 Input a variable as shown here: press and then press the key that
corresponds to the desired variable name.
*2 Pressing (RECALL) displays a screen that shows the values
currently assigned to variables A, B, C, D, E, F, M, x, and y. On this
screen, values are always displayed using the “Norm 1” Number
Format. To close the screen without recalling a variable value, press
.
Independent Memory (M)
You can add calculation results to or subtract results from independent
memory. The “M” appears on the display when there is any value other than
zero stored in independent memory.
To clear the contents of M
0(M) 0
To add the result of 10 × 5 to M
(Continuing) 10550
To subtract the result of 10 + 5 from M
(Continuing) 105(M−) 15
To recall the contents of M
(Continuing) (RECALL)(M)35
Note: Variable M is used for independent memory. You also can call M and
use it in a calculation you are inputting.
Clearing the Contents of All Memories
Ans memory, independent memory, and variable contents are retained even
if you press , change the calculation mode, or turn off the calculator.
Perform the procedure below when you want to clear the contents of all
memories.
(RESET)(Memory)(Yes)
Function Calculations
Note: To interrupt an ongoing calculation before its result appears, press
.
12

Pi π:πis displayed as 3.141592654, but π= 3.14159265358980 is used for
internal calculations.
Natural Logarithm Base e:eis displayed as 2.718281828, but e=
2.71828182845904 is used for internal calculations.
sin, cos, tan, sin-1, cos-1, tan-1:Specify the angle unit before performing
calculations.
sin 30° = 1
2(Angle Unit: Degree) 30 1 2
sinh, cosh, tanh, sinh-1, cosh-1, tanh-1: Input a function from the menu that
appears when you press (Hyperbolic Func)*1. The angle unit setting
does not affect calculations.
*1 Depending on the calculation mode, you should press .
∘
,r,
g
:These functions specify the angle unit. ° specifies degree, rradian,
and ggradian. Input a function from the menu that appears when you
perform the following key operation: (Angle Unit)*2.
π/2 radians = 90° (Angle Unit: Degree)
(π)2(Angle Unit)(r)90
*2 Depending on the calculation mode, you should press .
,:Exponential functions.
e5× 2 = 296.8263182
(MathI/MathO) () 52296.8263182
(LineI/LineO) () 52296.8263182
log: Logarithmic function. Use to input logab as log (a, b). Base 10 is
the default setting if you do not input anything for a.
log101000 = log 1000 = 3 1000 3
log216 = 4 2(,) 16 4
The key also can be used for input, but only while MathI/MathO or
MathI/DecimalO is selected for Input/Output on the setup menu. In this
case, you must input a value for the base.
log216 = 4 2164
ln: Natural logarithm to base e.
ln 90 (= loge90) = 4.49980967 90 4.49980967
x2, x3,

,

,

, , x-1:Powers, power roots, and reciprocals.
(1 + 1)2+2 = 16 112216
(52)3= 15625 5 15625
32
5 = 2
(MathI/MathO) () 5322
(LineI/LineO) 5() 32 2
2×3 =3 2=4.242640687...
(MathI/MathO) 2332
(LineI/LineO) 234.242640687
Pol, Rec: Pol converts rectangular coordinates to polar coordinates, while
Rec converts polar coordinates to rectangular coordinates.
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• Specify the angle unit before
performing calculations.
• The calculation result for rand θ
and for xand yare each
assigned respectively to
variables xand y.
• Calculation result θis displayed
in the range of -180° < θ≦180°.
To convert rectangular coordinates 2, 2to polar coordinates (Angle
Unit: Degree)
(MathI/MathO) (Pol)2(,)2 r=2, θ=45
To convert polar coordinates 2, 45° to rectangular coordinates (Angle
Unit: Degree)
(MathI/MathO) (Rec)2(,) 45 x=1, y=1
x!: Factorial function.
(5 + 3) ! = 40320 53(x!)40320
Abs: Absolute value function.
|2 − 7| × 2 = 10
(MathI/MathO) 27210
(LineI/LineO) 27210
Ran#: Function that generates a pseudo random number in the range of
0.000 to 0.999. The result is displayed as a fraction when MathI/MathO is
selected for Input/Output on the setup menu.
To obtain random three-digit integers
1000(Ran#)459
(The result differs with each execution.)
RanInt#: Function that generates a pseudo random integer between a
specified start value and end value.
To generate random integers in the range of 1 to 6
(RanInt) 1(,) 6 2
(The result differs with each execution.)
nPr, nCr:Permutation (nPr) and combination (nCr) functions.
To determine the number of permutations and combinations possible when
selecting four people from a group of 10
Permutations: 10(nPr) 45040
Combinations: 10(nCr) 4210
Rnd: Using the Rnd function causes decimal fraction values of the
argument to be rounded in accordance with the current Number Format
setting. For example, the internal and displayed result of Rnd(10 ÷ 3) is
3.333 when the Number Format setting is Fix 3. Using the Norm 1 or Norm
2 setting cause the argument to be rounded off at the 11th digit of the
mantissa part.
To perform the following calculations when Fix 3 is selected for the number
of display digits: 10 ÷ 3 × 3 and Rnd(10 ÷ 3) × 3 (MathI/DecimalO)
(SETUP)(Number Format)(Fix)
103310.000
(Rnd) 10339.999
14

Statistical Calculations
Perform the steps below to start a statistical calculation.
1. Press , select the Statistics Mode icon, and then press .
2. On the Select Type screen that appears, select a statistical calculation
type.
To select this type of statistical calculation: Press this key:
Single-variable (x)(1-Variable)
Paired-variable (x, y), linear regression (y=a+bx)
Paired-variable (x, y), quadratic regression (y=a+bx+cx2)
Paired-variable (x, y), logarithmic regression (y=a+b･ln(x))
Paired-variable (x, y), eexponential regression (y=a･e^(bx))
Paired-variable (x, y), ab exponential regression (y=a･b^x)
Paired-variable (x, y), power regression (y=a･x^b)
Paired-variable (x, y), inverse regression (y=a+b/x)
• Performing any of the above key operations displays the Statistics
Editor.
Note: When you want to change the calculation type after entering the
Statistics Mode, perform the key operation (Select Type) to display
the calculation type selection screen.
Inputting Data with Statistics Editor
Statistics Editor displays one, two, or three columns: single-variable (x),
single variable and frequency (x, Freq), paired-variable (x, y), paired-
variable and frequency (x, y, Freq). The number of data rows that can be
input depends on the number of columns: 160 rows for one column, 80
rows for two columns, 53 rows for three columns.
Note
• Use the Freq (frequency) column to input the quantity (frequency) of
identical data items. Display of the Freq column can be turned on
(displayed) or off (not displayed) using the Statistics setting on the setup
menu.
• Pressing the key while the Statistics Editor is on the screen will
display a statistical calculation screen for performing calculations based
on the input data. What you need to do to return to the Statistics Editor
from the statistical calculation screen depends on the calculation type
you selected. Press (Data) if you selected single-variable or
(Data) if you selected paired-variable.
Ex 1: To select logarithmic regression and input the following data: (170,
66), (173, 68), (179, 75)
(Select Type)(y=a+b･ln(x))
170173179
666875
15

Important: All data currently input in the Statistics Editor is deleted
whenever you exit the Statistics Mode, switch between the single-variable
and a paired-variable statistical calculation type, or change the Statistics
setting on the setup menu.
To delete a line: In the Statistics Editor, move the cursor to the line that you
want to delete and then press .
To insert a line: In the Statistics Editor, move the cursor to the location
where you want to insert the line and then perform the following key
operation: (Editor)(Insert Row).
To delete all Statistics Editor contents: In the Statistics Editor, perform
the following key operation: (Editor)(Delete All).
Displaying Statistical Values Based On Input Data
From the Statistics Editor:
(1-Variable Calc or 2-Variable Calc)
From the statistical calculation screen:
(1-Variable Calc or 2-Variable Calc)
Displaying Regression Calculation Results Based On
Input Data (Paired-Variable Data Only)
From the Statistics Editor:
(Regression Calc)
From the statistical calculation screen:
(Regression Calc)
Obtaining Statistical Values from Input Data
You can use the operations in this section to recall statistical values
assigned to variables (σx, Σx2, etc.) based on the data you input with the
Statistics Editor. You can also use the variables in calculations. The
operations in this section are performed on the statistical calculation screen
that appears when you press while the Statistics Editor is displayed.
Supported statistical variables and the keys you should press to recall them
are shown below. For single-variable statistical calculations, the variables
marked with an asterisk (*) are available.
Summation: Σx*, Σx2*, Σy, Σy2, Σxy, Σx3, Σx2y, Σx4
(Summation) to 
Number of Items: n* / Mean: 𝑥
−*, 𝑦 −/ Population Variance: σ2x*, σ2y/
Population Standard Deviation: σx*, σy/ Sample Variance: s2x*, s2y/
Sample Standard Deviation: sx*, sy
(Variable) to ,  to 
Minimum Value: min(x)*, min(y) / Maximum Value: max(x)*, max(y)
When the single-variable statistical calculation is selected:
(Min/Max) , 
When a paired-variable statistical calculation is selected:
(Min/Max) to 
First Quartile: Q1* / Median: Med* / Third Quartile: Q3* (For single-variable
statistical calculations only)
(Min/Max) to 
Regression Coefficients: a, b/ Correlation Coefficient: r/ Estimated
Values: 𝑥, 𝑦
(Regression) to 
Regression Coefficients for Quadratic Regression: a, b, c/ Estimated
Values: 𝑥1, 𝑥2, 𝑦
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(Regression) to 
•𝑥, 𝑥1, 𝑥2and 𝑦are commands of the type that take an argument
immediately before them.
Ex 2: To input the single-variable data x= {1, 2, 2, 3, 3, 3, 4, 4, 5}, using the
Freq column to specify the number of repeats for each items {xn; freqn} =
{1;1, 2;2, 3;3, 4;2, 5;1}, and calculate the mean.
(SETUP)*1 or *2 (Statistics)(On)
*1: fx-82AR X *2: fx-95AR X
(Select Type)(1-Variable)
12345
1232
(Variable)(𝑥
−)3
Ex 3: To calculate the logarithmic regression correlation coefficients for the
following paired-variable data and determine the regression formula: (x, y) =
(20, 3150), (110, 7310), (200, 8800), (290, 9310). Specify Fix 3 (three
decimal places) for results.
(SETUP)*1 or *2 (Statistics)(Off)
*1: fx-82AR X *2: fx-95AR X
(SETUP)(Number Format)(Fix)
(Select Type)(y=a+b･ln(x))
20110200290
3150731088009310
(Regression)(r)0.998
(Regression)(a)-3857.984
(Regression)(b)2357.532
Calculating Estimated Values
Based on the regression formula obtained by paired-variable statistical
calculation, the estimated value of ycan be calculated for a given x-value.
The corresponding x-value (two values, x1and x2, in the case of quadratic
regression) also can be calculated for a value of yin the regression formula.
Ex 4: To determine the estimate value for ywhen x= 160 in the regression
formula produced by logarithmic regression of the data in Ex 3. Specify Fix
3 for the result. (Perform the following operation after completing the
operations in Ex 3.)
160(Regression)(𝑦)8106.898
Important: Regression coefficient, correlation coefficient, and estimated
value calculations can take considerable time when there are a large
number of data items.
Equation Calculations (fx-95AR X only)
Perform the steps below to solve an equation in the Equation/Func Mode.
1. Press , select the Equation/Func Mode icon, and then press .
2. Select the type of calculation you want to perform.
To select this calculation
type: Do this:
17

Simultaneous linear equations
with two, three, or four
unknowns
Press (Simul Equation), and then
use a number key (to ) to
specify the number of unknowns.
Quadratic equations, cubic
equations, or quartic equations
Press (Polynomial), and then use
a number key (to ) to specify
the polynomial degree.
3. Use the Coefficient Editor that appears to input coefficient values.
• To solve 2x2+ x− 3 = 0, for example, press (Polynomial)in
step 2. Use the Coefficient Editor that appears to input
213.
• Pressing will clear all of the coefficients to zero.
4. After all the values are the way you want, press .
• This will display a solution. Each press of will display another
solution. Pressing while the final solution is displayed will return to
the Coefficient Editor.
• A message appears to let you know when there is no solution or when
there are infinite solutions. Pressing or will return to the
Coefficient Editor.
• You can assign the currently displayed solution to a variable. While
the solution is displayed, press and then the key that
corresponds to the name of the variable to which you want to assign
it.
• To return to the Coefficient Editor while any solution is displayed,
press .
Note: Solutions that include √are displayed only when the selected
calculation type is Polynomial.
To change the current equation type setting: Press (Simul
Equation) or (Polynomial), and then press , , or . Changing
the equation type causes the values of all Coefficient Editor coefficients to
change to zero.
Equation/Func Mode Calculation Examples
x+ 2y= 3, 2x+ 3y= 4
(Simul Equation)
123234


(x=)
(y=)
-1
2
x2+ 2x− 2 = 0
(Polynomial)
122

(x1=)
(x2=)
-1 + 3
-1 − 3
(Displays x-coordinate of local minimum of y= x2+ 2x− 2.*)
(x=) -1
(Displays y-coordinate of local minimum of y= x2+ 2x− 2.*)
(y=) -3
* The x- and y-coordinates of the local minimum (or local maximum) of the
function y= ax2+ bx + care also displayed, but only when a quadratic
equation is selected for the calculation type.
18

Creating a Number Table
The Table Mode generates a number table based on one or two functions.
Example: To generate a number table for the functions 𝑓𝑥=𝑥
2+1
2and
g𝑥=𝑥
2−1
2for the range -1 ≦ 𝑥 ≦ 1, incremented in steps of 0.5
1. Press , select the Table Mode icon, and then press .
2. Configure settings to generate a number table from two functions.
(SETUP)*1 or *2 (Table)(f(x),g(x))
*1: fx-82AR X *2: fx-95AR X
3. Input 𝑥2+1
2.
(x)12
4. Input 𝑥2−1
2.
(x)12
5. Press . On the Table Range dialog box that appears, input values for
Start (Default: 1), End (Default: 5), and Step (Default: 1).
110.5
6. Press to generate the number table.
• Press to return to the screen in
step 3.
Tip
• In the number table shown in step 6, you can change the value in the
currently highlighted xcell. Changing the xvalue causes the f(x) and g(x)
values in the same line to be updated accordingly.
• If there is value in the xcell above the currently highlighted xcell,
pressing or automatically inputs into the highlighted cell the
value equal to the value of the cell above it plus the step value. So also,
pressing automatically inputs the value equal to the value of the cell
above less the step value. The f(x) and g(x) values in the same line are
also updated accordingly.
Note
• After pressing in step 4 above, proceeding from step 5 onwards
without inputting anything for g(x)will generate a number table for f(x)
only.
• The maximum number of rows in the generated number table depends
on the setup menu table setting. Up to 45 rows are supported for the
“f(x)” setting, while 30 rows are supported for the “f(x),g(x)” setting.
• The number table generation operation causes the contents of variable x
to be changed.
Important: Functions input in this mode are deleted whenever the Input/
Output settings are changed in the Table Mode.
19