fx-85W fx-85WA fx-300W fx-350TL
Users Guide Gua del usuario Mode demploi Bedienungsanleitung Guida dellutilizzatore
ENGLISH Removing and Replacing the Calculators Cover

To Remove the cover

Grasp the top of the cover, and slide the unit out from the bottom.

To Replace the cover

Grasp the top of the cover, and slide the unit in from the bottom. Always slide the unit into the cover with the units display end first. Never slide the keyboard end of the unit into the cover.

Safety Precautions

Be sure to read the following safety precautions before using this calculator. Keep this manual handy for later reference.

Caution

This symbol is used to indicate information that can result in personal injury or material damage if ignored.

Batteries

After removing the batteries from the calculator, put
them in a safe place where there is no danger of them getting into the hands of small children and accidently swallowed. Keep batteries out of the reach of small children. If accidently swallowed, consult with a physician immediately. Never charge batteries, try to take batteries apart, or allow batteries to become shorted. Never expose batteries to direct heat or dispose of them by incineration. Misuse of batteries can cause them to leak acid that can cause damage to nearby items and creates the possibility of fire and personal injury. Always make sure that a batterys positive k and negative l sides are facing correctly when you load it into the calculator. Remove the batteries if you do not plan to use the calculator for a long time. Use only the type of batteries specified for this calculator in this manual.
Disposing of the Calculator
Never dispose of the calculator by burning it. Doing
so can cause certain components to suddenly burst, creating the danger of fire and personal injury.
The displays and illustrations (such as key markings)
shown in this Users Guide are for illustrative purposes only, and may differ somewhat from the actual items they represent. The contents of this manual are subject to change without notice. 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 these materials. Moreover, CASIO Computer Co., Ltd. shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.

Handling Precautions

Be sure to press the P button on the back of the cal
culator (step 6 on page 29) before using it for the first time (fx-350TL). Be sure to press the 5 key before using the calculator for the first time (fx-85W/fx-85WA/fx-300W). Even if the calculator is operating normally, replace the battery at least once every three years. Dead battery can leak, causing damage to and malfunction of the calculator. Never leave the dead battery in the calculator. The battery that comes with the calculator when you purchase it is for testing only. It may not provide full service life. Low battery power can cause memory contents to become corrupted or lost completely. Always keep written records of all important data. E-2
Avoid use and storage in areas subjected to temperature extremes. Very low temperatures can cause slow display response, total failure of the display, and shortening of battery life. Also avoid leaving the calculator in direct sunlight, near a window, near a heater or anywhere else it might become exposed to very high temperatures. Heat can cause discoloration or deformation of the calculators case, and damage to internal circuitry. Avoid use and storage in areas subjected to large amounts of humidity and dust. Take care never to leave the calculator where it might be splashed by water or exposed to large amounts of humidity or dust. Such elements can damage internal circuitry. Never drop the calculator or otherwise subject it to strong impact. Never twist or bend the calculator. Avoid carrying the calculator in the pocket of your trousers or other tight-fitting clothing where it might be subjected to twisting or bending. Never try to take the calculator apart. Never press the keys of the calculator with a ball-point pen or other pointed object. Use a soft, dry cloth to clean the exterior of the unit. If the calculator becomes very dirty, wipe it off with a cloth moistened in a weak solution of water and a mild neutral household detergent. Wring out all excess moisture before wiping the calculator. Never use thinner, benzine or other volatile agents to clean the calculator. Doing so can remove printed markings and damage the case.

Contents

Safety Precautions.. 1 Handling Precautions.. 2 Two-line Display.. 5 Key Layout... 6 Before Starting Calculations.. 8
kModes... 8 kInput Capacity... 9 kMaking Corrections During Input.. 9 kReplay Function... 9 kError Locator... 9 kExponential Display Formats. 10 kAnswer Memory... 10
Basic Calculations... 11 Memory Calculations.. 11
kIndependent Memory.. 11 kVariables.. 11
Fraction Calculations.. 12
kFraction Calculations.. 12 kDecimal-to-Fraction Conversion.. 12 kFraction-to-Decimal Conversion.. 12
Percentage Calculations.. 13 Scientific Function Calculations. 14
kTrigonometric/Inverse Trigonometric Functions. 14 kHyperbolic/Inverse Hyperbolic Functions. 15 kAngle Unit Conversion... 15 kCommon and Natural Logarithms/ Antilogarithms.. 15 kSquare Roots, Cube Roots, Roots, Squares, Cubes, Reciprocals, Factorials, Random Numbers and .. 16 kFIX, SCI, RND... 16 kENG Calculations.. 17 kCoordinate Conversion (Pol(x, y), Rec (r, )). 18 E-4
kPermutation... 18 kCombination.. 18
Statistical Calculations.. 19
kStandard Deviation (SD Mode).. 19 kRegression Calculations (REG Mode).. 20
Formula Memory (fx-85W ).. 23 Base-n Calculations (fx-85W ).. 23 Degrees, Minutes, Seconds Calculations. 25 Technical Information.. 25
kWhen you have a problem.. 25 kError Messages... 26 kOrder of Operations.. 27 kStacks... 27 kPower Supply.. 28 kInput Ranges.. 30

Specifications.. 32

Two-line Display
You can simultaneously check the calculation formula and its answer.
The first line displays the calculation formula. The second line displays the answer.

Key Layout Key Layout

<fx-350TL>

REPLAY

Page Page Page Page Page Page Page

sin-1 D

cos-1 E

tan-1 F

Page Page

McI ScI

Page fx-85WA/fx-300W:

Key Layout

< fx-85W >

MODE ON

x! LOGIC

10 BIN

Before Starting Calculations.

k Modes

Application Calculation Modes Normal calculations Standard deviation calculations Regression calculations Base-n calculations (fx-85W only) COMP SD SD Mode Name Mode Indicator

REG REG BASE-N b (binary) o (octal) d (decimal) H (hexadecimal) DEG RAD GRA
Angle Unit Modes Degrees Radians Grads Display Modes Exponential notation (Canceling FIX and SCI specification) Number of decimal place specification Number of significant digit specification

Fix Sci

NORM1 NORM2 FIX SCI
Mode indicators appear in the lower part of the display, except for the Base-n indicators which appear in the exponent part of the display. You cannot set the angle unit or the display mode while the calculator is in the BASE-N mode (fx-85W). The COMP, SD, and REG modes can be used in combination with the angle unit modes. Be sure to check the current calculation mode (SD, REG, COMP) and angle unit mode (DEG, RAD, GRA) before beginning a calculation. E-8

k Input Capacity

The memory area used for calculation input can hold 79 steps. Whenever you input the 73rd step of any calculation, the cursor changes from _ to k to let you know memory is running low. If you still need to input more, you should divide your calculation into two or more parts.
k Making Corrections During Input
Use e and r to move the cursor to the location you want. Press [ to delete the number or function at the current cursor position. Press A K to change to an insert cursor t. Inputting something while the insert cursor is on the display inserts the input at the insert cursor position. Press e, r, A K, or = returns to the normal cursor from the insert cursor.

k Replay Function

Pressing r or e recalls the last calculation you performed. You can then make any changes you want in the calculation and re-execute it. Pressing t does not clear Replay memory, so you can recall the last calculation even after you press t. Replay memory is cleared whenever you start a new calculation, change to another mode, or turn off power.

k Error Locator

Pressing r or e after an error occurs displays the calculation with the cursor positioned at the location where the error occurred.
k Exponential Display Formats
This calculator can display up to 10 digits. Larger values are automatically displayed using exponential notation. In the case of decimal values, you can select between two formats that determine at what point exponential notation is used. Press F F F F (or 2) to select NORM 1 or NORM 2 (fx-85W). For other models, press F F F (or 2).

NORM 1

With NORM 1, exponential notation is automatically used for integer values with more than 10 digits and decimal values with more than two decimal places.

NORM 2

With NORM 2, exponential notation is automatically used for integer values with more than 10 digits and decimal values with more than nine decimal places. All of the examples in this manual show calculation results using the NORM 1 format.

k Answer Memory

Whenever you press = after inputting values or an expression, the calculated result is automatically stored in Answer Memory. You can recall Answer Memory contents by pressing g. Answer Memory can store up to 12 digits for the mantissa and two digits for the exponent. Answer Memory contents are not changed if the operation performed by any of the above key operations results in an error.

Basic Calculations

Use the COMP mode for basic calculations. Example 1 : 3(5109) 3-R5eD9T= Example 2 : 5(97) 5-R9+7T= You can skip all T operations before =.

1.5-08

Memory Calculations

k Independent Memory

Values can be input directly into memory, added to memor y, or subtracted from memory. Independent memory is convenient for calculating cumulative totals. Independent memory uses the same memory area as variable M. To clear independent memory (M), input 0 j 3. Example: ) 90 (Total) + 9 j , 6 | 45 - 2 A {

32.00 47.00 90.00 11.00

k Variables
There are nine variables (A through F, M, X and Y), which can be used to store data, constants, results, and other values. Use the following operation to delete data assigned to all nine variables: A C =. Use the following operation to delete data assigned to a particular variable: 0 j 1. This operation deletes the data assigned to variable A. E-11
Example: 193.8.4 193.6.9 193.2 j 1 \ 23 =

8.400 6.900

p 1 \ 28 =

Fraction Calculations

k Fraction Calculations
Use the COMP mode for fraction calculations. Values are automatically displayed in decimal format whenever the total number of digits of a fractional value (integer numerator denominator separator marks) exceeds 10. Example 1 : 5
2C3 +1C 4C 5= Example 2 : 1 1.1 C 2 + 1.6 =
Fraction/decimal calculation results are always decimal.
k Decimal-to-Fraction Conversion

Example: 2.2.75 =

2.3 4.4.00
k Fraction-to-Decimal Conversion
Example: 1 0.5 (Fraction Decimal) 2 1C 2= E-12

1 2. 00

0.2. 00

Percentage Calculations

Use the COMP mode for percentage calculations. Example 1 : To calculate 12% of - 12 A v

180.00

Example 2 : To calculate what percentage of 880 is \ 880 A v Example 3 : To add 15% onto - 15 A v + Example 4 : To discount 3500 by 25% 3500 - 25 A v ,

2875.00

2625.00
Example 5: If 300 grams are added to a test sample originally weighing 500 grams, what is the percentage increase in weight? (%) + 500 A v

160.00

Example 6: If temperature changes from 40C to 46C, what percentage did it rise? (%) , 40 A v
Scientific Function Calculations
Use the COMP mode for scientific function calculations. = 3.14159265359
k Trigonometric/Inverse Trigonometric Functions
Example 1 : sin6352o41 fx-85W: q q q 1 R Other models: q q 1
00 S 63 I 52 I 41 I = 0.897859012 R

Example 2 : cos

rad 3 fx-85W: q q q 2 T Other models: q q 2

WRAx\3T=

2 Example 3 : cos rad fx-85W: q q q 2 T Other models: q q 2
00 A V R L 2 \ 2 T = 0.785398163 T
Example 4 : tan1 0.741 fx-85W: q q q 1 R Other models: q q 1

0.2500

00 A g 0.741 = 36.53844577 R
k Hyperbolic/Inverse Hyperbolic Functions

Example 1 : sinh 3.6

M S 3.6 = 18.2854553600

Example 2 : sinh1 30

M A j 30 = 4.09462222400

k Angle Unit Conversion

Press A v to display the following menu.
Pressing 1 , 2 , or 3 converts the displayed value to the corresponding angle unit. Example : To convert 4.25 radians to degrees fx-85W: q q q 1 R Other models: q q 1 4.25 A v 2 (R ) = 243.5070629

4. 25 r

k Common and Natural Logarithms/ Antilogarithms

Example 1 : log 1.23

R 1.23 =

0.08990511100

Example 2 : In 90 (loge 90)

T 90 =

Example 3 : e10 Example 4 : 101.5 Example 5 : 24
4.4998096700 22026.4657900 31.622776600 16.00

A U 10 = A Q 1.5 =

2w 4= E-15
k Square Roots, Cube Roots, Roots, Squares, Cubes, Reciprocals, Factorials, Random Numbers and

Example 1: 5

L2 +L3 -L 5=

Example 2: 3 27

5.28719690900
D 5 + D D 27 = 1.29002405300

Example 3:

123 ( = ) 7 A H 123 =

1.98864779500

Example 4: 123 + 30 K = Example 5: Example 6: N =

1023.00 1728.00

R 3a ,4 a T a =

Example 7: 8! 8Af=

12.00 40320.00
Example 8: To generate a random number between 0.000 and 0.999

Example 9: 3 3Ax=

0.66400 9.42477796100
Example (results differ each time)

k FIX, SCI, RND

Example 1: \ 7 - 14 = E-16

400.00

(Specifies three decimal places.)
fx-85W: F F F F Other models: q q q 1 3
(Calculation continues using 10 display digits)

400.00000

200 \ 7 =

28.57100 400.00000

- 14 =
Performing the same calculation using the specified number of decimal places 200 \ 7 =

(Internal rounding)

28.57100 28.57100 399.994 00

AQ - 14 =

Press F F F F (fx-85W) to clear FIX specification. For other models, press F F F 3 1. Example 2: 1 3, displaying result with two significant digits (SCI 2) fx-85W: q q q q Other models: q q q 1 \3=
Press F F F F (fx-85W) to clear SCI specification. For other models, press F F F 3 1.

k ENG Calculations

Example 1: To convert 56,088 meters to kilometers 56088 = J

56.088003

Example 2: To convert 0.08125 grams to milligrams 0.08125 = J

81.2503

k Coordinate Conversion (Pol(x, y), Rec (r, ))
Calculation results are automatically assigned to variables E and F. Example 1: To convert polar coordinates (r2, 60) to rectangular coordinates (x, y) (DEG mode) x y

A F 2 P 60 T = 0o

1.73205080800
0 n , 0 o swaps displayed value with value in memory. Example 2: To convert rectangular coordinates (1, 3) to polar coordinates (r, ) (RAD mode) r

f1P L3T=

0 o 1.04719755100
0 n , 0 o swaps displayed value with value in memory.

k Permutation

Example: To determine how many different 4-digit values can be produced using the numbers 1 through 7 Numbers cannot be duplicated within the same 4-digit value (1234 is allowed, but 1123 is not). 7Am 4=

k Combination

Example: To determine how many different 4-member groups can be organized in a group of 10 individuals 10 n 4 = (fx-85W: A n) E-18

Statistical Calculations

k Standard Deviation (SD Mode)
Press F F 1 (fx-85W) to enter the SD Mode for statistical calculations using standard deviation. For other models, press F 2. Data input always starts with A m = to clear statistical memory. Input data is used to calculate values for x2 n, x, x2, o, n and n-1 which you can x recall using the key operations noted 0 k n nearby. AM o

A A n A N n-1

Example: To calculate n1 , n, o, n, x, and x2 for the following data : 55, 54, 51, 55, 53, 53, 54, 52 Enter SD Mode fx-85W: F F 1 Other models: F 2
A m = (Memory Clear) 55 S 54 S 51 S 55 S 53 S S 54 S 52 S
(Sample Standard Deviation n1 ) (Population Standard Deviation n) (Arithmetic Mean o) (Number of Data n) (Sum of Values x) (Sum of Squares of Values x 2)

A N= A A= AM = 0k 0H 0G

1.40788595300 1.31695671900 53.37500 8.00 427.00 22805.00
Data Input Precautions S S inputs the same data twice.
You can also input multiple entries of the same data using A G. To input the data 110 ten times, for example, press 110 A G 10 S. The above results can be obtained in any order, and not necessarily that shown above. To delete data you have just input, press A U.
k Regression Calculations (REG Mode)
Press F F 2 (fx-85W) to enter the REG mode and then select one of the following regression types. For other models, press F 3.

1: 2: 3: r 1: r 2: r 3:

Linear regression Logarithmic regression Exponential regression Power regression Inverse regression Quadratic regression
Data input always starts with A m = to clear statistical memory. The values produced by a regression calculation depend on the values input, and results can be recalled using the key operations shown in the table below.
0 G x 2 A N 0 H x A l 0k n Ad 0 h y 2 A c 0 n y A q 0 o xy A w 0 M x 3 A e 0 x x2y A u 0 y x 4 A O AM o Ab A A xn

xn-1 p yn yn-1

Regression coefficient A Regression coefficient B Regression coefficient C Correlation coefficient r

Linear Regression

The regression formula for linear regression is: y A Bx. Example: Atmospheric Pressure vs. Temperature
Temperature Atmospheric Pressure

10C 15C 20C 25C 30C

1003 hPa 1005 hPa 1010 hPa 1011 hPa 1014 hPa
Perform linear regression to determine the regression formula terms and correlation coefficient for the data nearby. Next, use the regression formula to estimate atmospheric pressure at 18C and temperature at 1000 hPa.
Enter REG Mode (Linear Regression) fx-85W: q q Other models: q A m = (Memory Clear) 10 P 1003 S 15 P 1005 S 20 P 1010 S 25 P 1011 S 30 P 1014 S

(Regression Coefficient A) (Regression Coefficient B) (Correlation Coefficient r ) (Atmospheric Pressure at 18C) (Temperature at 1000 hPa)

Aq= Aw= AJ=

18 A b 1000 A O
997.400 0.5600 0.98260736800 1007.4800 4.64285714300

Quadratic Regression

The regression formula for quadratic regression is: y = A + Bx +C x2. Input data using the following key sequence. < x-data> P <y-data> S

Example:

1.6 23.5 38.0 46.4 48.0
Perform quadratic regression to determine the regression formula terms and correlation coefficient for the data nearby. Next, use the regression fory mula to estimate the values for (esx timated value of y) for xi = 16 and (estimated value of x) for yi = 20.
Enter REG mode (Quadratic regression) fx-85W: F F 2 r 3 Other models: q 3 r 3
29 P 1.6 S 50 P 23.5 S 74 P 38.0 S103 P 46.4 S 118 P 48.0 S
(Regression Coefficient A) (Regression Coefficient B) (Regression Coefficient C) ( when x i = 16) y ( 1 when yi = 20) x ( 2 when yi = 20) x

A q = -35.59856934 Aw=

1.495939413

A e = -6.71629667-03

16 A b -13.A O

47.14556728 175.5872105

You can also input multiple entries of the same data using A G. To input the data 20 and 30 five times, for example, press 20 P 30 A G 5 S. The above results can be obtained in any order, and not necessarily that shown above. To delete data you have just input, press A U.

Formula Memory

(fx-85W)
Formula memory lets you input a single formula in memory, and then input values for the formula's variables to calculate results. Memory can hold a single formula, up to 79 steps long. This function can be used in the COMP mode only. Note that the formula is actually stored in memory when you press the C key in the sequence below. Example: To save the following formula, recall it, and then use it to calculate a result: Y = X2 + 3X 12 Input the formula.

p yp u px K+ 3 p x , 12

Store it in memory. Input a value for its variable.

Y= X 2 +3 X-12

0. 58.
Formula memory is cleared whenever you start a new calculation, change to another mode, or turn off power.
Base-n Calculations (fx-85W)
In addition to decimal values, calculations can be performed using binary, octal and hexadecimal values. You can specify the default number system to be applied to all input and displayed values, and the number system for individual values you input. You cannot use scientific functions in binary, octal, decimal, and hexadecimal calculations. You cannot input values that include decimal part and an exponent. If you input a value that includes a decimal part, the unit automatically cuts off the decimal part. Negative binary, octal, and hexadecimal values are produced by taking the two's complement. E-23

You can use the following logical operators between values in Base-n calculations: and (logical product), or (logical sum), xor (exclusive logical sum), xnor (exclusive logical sum negation), Not (negation), and Neg (minus). The following are the allowable ranges for each of the available number systems. Binary Octal Decimal 2147483648 Hexadecimal 80000000 0

x x x x x x x

2147483647 FFFFFFFF 7FFFFFFF
Example 1: To perform the following calculation and produce a binary result: 101112 + 110102 Binary mode

101112 + 110102

0. 0. 110001.
Example 2: To perform the following calculation and produce an octal result: Octal mode

0. 0. 516.

l l l 4 (o) 76548 \ l l l 1 (d)1210 =
Example 3: To perform the following calculation and produce a hexadecimal result: or 11012 Hexadecimal mode

0. 0. 12d.

12016 l 2 (or) l l l 3 (b)11012
Degrees, Minutes, Seconds Calculations
You can perform sexagesimal calculations using degrees (hours), minutes, and seconds, and convert between sexagesimal and decimal values. Example 1: To convert the decimal value 2.258 to a sexagesimal value 2.258 =

2.258 21528.8

123456 3.I 34 I 56 I - 3.45
Example 2: To perform the following calculation:

0. 432431.2

Technical Information
k When you have a problem.
If calculation results are not what you expect or if an error occurs, perform the following steps. 1. F 1 (COMP mode) 2. fx-85W: F F F 1 (DEG mode) Other models: q q 1 3. fx-85W: F F F F (NORM 1 mode) Other models: F F F 4. Check the formula you are working with to confirm it is correct. 5. Enter the correct modes to perform the calculation and try again. < fx-350TL> If the above steps do not correct your problem, press the P button (see page 29) on the back of the calculator to reset it. Pressing the P button deletes all data stored in calculator memory. Make sure you always keep written copies of all important data. E-25
< fx-85W/ fx-85WA / fx-300W > If the above steps do not correct the problem, press the 5 key. The calculator performs a self-check operation and deletes all data stored in memory if any abnormality is detected. Make sure you always keep written copies of all important data.

k Error Messages

The calculator is locked up while an error message is on the display. Press t to clear the error, or press e or r to display the calculation and correct the problem. See Error Locator on page 9 for details.

Ma ERROR

Cause Calculation result is outside the allowable calculation range. Attempt to perform a function calculation using a value that exceeds the allowable input range. Attempt to perform an illogical operation (division by zero, etc.). Action Check your input values and make sure they are all within the allowable ranges. Pay special attention to values in any memory areas you are using.

Stk ERROR

Cause Capacity of the numeric stack or operator stack is exceeded. Action Simplify the calculation. The numeric stack has 10 levels and the operator stack has 24 levels. Divide your calculation into two or more separate parts.

Syn ERROR

Cause Attempt to perform an illegal mathematical operation. Action Press e or r to display the calculation with the cursor located at the location of the error. Make necessary corrections. E-26

Arg ERROR

Cause Improper use of argument Action Press e or r to display the location of the cause of the error and make required corrections.

k Order of Operations

Calculations are performed in the following order of precedence. 1 Coordinate transformation: Pol ( x, y), Rec (r, ) 2 Type A functions: With these functions, the value is entered and then the function key is pressed. x2, x1, x!, 3 Powers and roots: xy, x 4 a b/c 5 Abbreviated multiplication format in front of , memory name, or variable name: 2, 5A, A etc. 6 Type B functions: With these functions, the function key is pressed and then the value is entered. 3 , , log, In, ex, 10x, sin, cos, tan, sin 1 , cos1, tan1, sinh, cosh, tanh, sinh 1, cosh1, tanh1, () 7 Abbreviated multiplication format in front of Type B functions: 2 3, Alog2 etc. 8 Permutation and combination: nPr, nCr 9 , 0 , * Operations of the same precedence are performed from 120 ex{In( 120)} right to left. exIn Other operations are performed from left to right. * Operations enclosed in parentheses are performed first.

k Stacks

This calculator uses memory areas, called stacks, to temporarily store values (numeric stack) and commands (command stack) according to their precedence during calculations. The numeric stack has 10 levels and the command stack has 24 levels. A stack error (Stk ERROR) occurs whenever you try to perform a calculation that is so complex that the capacity of a stack is exceeded. E-27

k Power Supply

The type of battery you should use depends on the model number of your calculator. < fx-85W/ fx-85WA / fx-300W> The TWO WAY POWER system actually has two power supplies: a solar cell and a G13 Type (LR44) button battery. Normally, calculators equipped with a solar cell alone can operate only when relatively bright light is present. The TWO WAY POWER system, however, lets you continue to use the calculator as long as there is enough light to read the display.

Replacing the Battery

Either of the following symptoms indicates battery power is low, and that the battery should be replaced. Display figures are dim and difficult to read in areas where there is little light available. Nothing appears on the display when you press the 5 key.

To replace the battery

1 Remove the six screws that hold the back cover in place and then remove the back Screw cover. 2 Remove the old battery. 3 Wipe off the sides of new battery with a dry, soft cloth. Load it into the unit with the positive k side facing up (so you can see it). 4 Replace the back cover and secure it in place with the six screws. 5 Press 5 to turn power on. Be sure not to skip this step.
< fx-350TL> This calculator is powered by single G13 Type (LR44) button 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 1 Press i to turn power off.
2 Remove the two screws that hold the battery cover in place and then remove the battery cover. 3 Remove the old battery. 4 Wipe off the side of new battery with a dry, soft cloth. Load it into the unit with the positive k side facing up (so you can see it). 5 Replace the battery cover and secure it in place with the two screws. 6 Use a thin, pointed object to press the P button. Be sure not to skip this step. 7 Press L to turn power on.

P button

Auto Power Off
Calculator power automatically turns off if you do not perform any operation for about six minutes. When this happens, press L ( fx-85W/ fx-85WA / fx-300W : 5 ) to turn power back on.

k Input Ranges

Internal digits: 12 Accuracy: As a rule, accuracy is 1 at the 10th digit. Functions sinx Input Range DEG 0 x 4.4999999991010 RAD 0 x 785398163.3 GRA 0 x 4.4999999991010 cosx DEG 0 x 4.5000000081010 RAD 0 x 785398164.9 GRA 0 x 5.0000000091010 tan x DEG Same as sinx, except when x= (2n-1)90. RAD Same as sinx, except when x= (2n-1)/2. GRA Same as sinx, except when x= (2n-1)100. sin1x cos1x tan1x sinhx coshx sinh x
0 x x 9.x 230.x 4.x 9.99999999910-1

cosh1x tanhx tanh1x 10 x

log x/ln x 0 x 9.9999999991099 x 99.99999999 9.9999999991099 x 230.x x x ; x G 0 x 0 x 69 (x is an integer)

ex x x2 1/x 3 x x!

Functions

Input Range

nP r 0 n 99, r n (n, r is an integer) 1 {n!/( nr)!} 9.nCr 0 n 99, r n (n, r is an integer) 49 Pol(x, y) x, y 9.99999999910 (x2 +y2 ) 9.99 Rec(r, ) 0 r 9.99999999910 : Same as sinx, cosx
a, b, c b, c x110100 Decimal Sexagesimal Conversions x x0: 110100ylogx100 x0: yx0: yn, 2n+1 ( n is an integer) However: ylogx100 y0: x G 0 1101001/x logy100 y0: xy0: x2n1, n (n G 0; n is an integer) However: 1/x logy100 Total of integer, numerator, and denominator must be 10 digits or less (including division marks). x 11050 y 11050 n 110100 xn, yn, o, p A, B, r : n G 0 xn1, yn1 : n G 0, 1

SD (REG)

* Erros are cumulative with such internal continuous calx 3 culations as x y, x , x!, and x , so accuracy may be adversely affected.

Specifications

Power Supply: fx-85W/ fx-85WA / fx-300W: Solar cell and a single G13 Type button battery (LR44) fx-350TL: Single G13 Type button battery (LR44) Battery Life: fx-85W/ fx-85WA / fx-300W: Approximately 3 years (1 hour use per day). fx-350TL: Approximately 12,000 hours continuous display of flashing cursor. Approximately 3 years when left with power turned off. Dimensions: 10(H)i76(W)i150(D) mm 3 / 8 (H)i3(W)i/8 (D) Weight: fx-85W/ fx-85WA / fx-300W: 80 g (2.8 oz) including battery fx-350TL: 90 g (3.2 oz) including battery Power Consumption: 0.0001W Operating Temperature: 0C ~ 40C (32F ~ 104F)
CASIO ELECTRONICS CO., LTD. Unit 6, 1000 North Circular Road, London NW2 7JD, U.K.

CASIO COMPUTER CO., LTD.

6-2, Hon-machi 1-chome Shibuya-ku, Tokyo 151-8543, Japan

U.S. Pat. 4,410.956

SA9810-B Printed in China Imprim en Chine HA310667-1

Finding a Mean and Standard Deviation on the Casio fx-85WA calculator. Suppose that we have 3 data values: 1, 2, 6 Switch to SD mode: MODE 2 Clear memory store: Shift Scl (yellow) = Enter data: 1 DT (blue) 2 DT 6 DT Find mean: Shift x (yellow) Find standard deviation: Shift xn1

(yellow)

The values stored in the memories can also be retrieved. Sample size n: RCL C (red) Sum of the values x: RCL B (red) Sum of squared values x2 : RCL A (red)
Finding a Mean and Standard Deviation on the Casio fx-85MS calculator. Suppose that we have 3 data values: 1, 2, 6 Switch to SD mode: MODE 2 Clear memory store: Shift CLR (yellow) 1 = Enter data: 1 DT (blue) 2 DT 6 DT Find mean: Find sample s.d.: The values stored Sample size n: x: x2 : Shift S-VAR (yellow) 1 = Shift S-VAR (yellow) 3 = in the Shift Shift Shift memories can also be retrieved. S-SUM (yellow) 3 = S-SUM (yellow) 2 = S-SUM (yellow) 1 =
Standard Deviation Examples: In each case, the mean is 5.0 Sample data: 5, 5, 5 Standard Deviation = 0.0 Sample data: 4, 5, 6 Standard Deviation = 1.0 Sample data: 1, 5, 9 Standard Deviation = 4.0 Sample data: 1, 1, 5, 9, 9 Standard Deviation = 4.0
Sample data: 1, 1, 5, 5, 9, 9 Standard Deviation = 3.58 Sample data: 1, 2, 3, 4, 5, 6, 7, 8, 9 Standard Deviation = 2.74
Sample v. Population Standard Deviation Recall that the method of calculating the sample standard deviation uses the divisor (n 1). If we know the exact value of the population mean, it is better to use this instead of the sample mean x and to then divide by n instead of by (n 1). This is called the Population Standard Deviation. In practice, this only happens if every member of the population has been measured, which is only rarely the case. The term Standard Deviation on its own almost always refers to the Sample S.D. If n is small, it is misleading to use the wrong divisor, so claims that the whole population has been measured should be treated with suspicion. This is especially so if statistical comparisons are to be made with other populations. Example: Suppose that I wish to investigate the retail price of widgets. I wish to know the average price and whether the price varies between shops. I visit a local shop and nd that they cost 1.29. If I have no other information, my estimate of the true average selling price is 1.29. 0 The sample standard deviation calculation = ; in other words, we have no information about the 0 variability. 0 Population standard deviation formula = = 0; in other words, the estimate suggests that the 1 price does not vary. This is not a very sensible conclusion! However, if I know in advance that the average selling price throughout the country is 1.29, then my single sample value provides some evidence that the price does not vary.
Properties of Mean and S.D. If data values are roughly symmetrical about the mean, then: Approximately 2 will be within 1 s.d. of the mean 3 Approximately 95% will be within 2 s.d. of mean Usually all will be within 3 s.d. of the mean The Inter-Quartile Range will be approximately 1.35 standard deviations.
Example: Undergraduate heights (data set M) n = 100 Mean = 1.6966 Standard Deviation = 0.1123 x 1 s.d. = (1.5843, 1.8089) Expect 67 in interval; Observe 67 x 2 s.d. = (1.4721, 1.9211) Expect 95 in interval; Observe 97 x 3 s.d. = (1.3598, 2.0334) Expect 100 in interval; Observe 100
Properties of Mean and S.D. If all the data values are identical, the standard deviation will be zero. In all other cases the standard deviation will be greater than zero (i.e. a positive value). If a constant is added to all the data values, the Mean is increased by the same constant; the S.D. is unchanged. If all the data values are multiplied by a constant, the Mean and S.D. are both multiplied by the same constant. Example: Temperature conversion from C to F. Need to multiply by 1.8 and add 32. Celsius Mean = 15 C and S.D. = 5.5 C Fahrenheit Mean = 15 1.8 + 32 = 59 F Fahrenheit S.D. = 5.5 1.8 = 9.9 F OUTLIERS An Outlier is an observation which is far away from most of the other data values. If an outlier is present then: the data value should be checked, if possible, by going back to the original records. if the value does appear to be genuine, consider if the data values should be transformed in some way. the outlier could be omitted, but only as a last resort if it is believed that it will seriously distort the summary statistics. The routine deletion of outliers is highly dangerous. If there is more than one apparently genuine outlier present, the risk of drawing wrong conclusions by deleting these values is greatly increased.
Detection of Outliers If the sample mean x and the sample standard deviation have been calculated, then for each xi it is possible to calculate a Standardised Variate: xi x s This measures how many standard deviations xi is away from the sample mean. If the absolute value of this is large (e.g. > 3) then xi could be considered to be an outlier. Minitab uses the quartiles and the inter-quartile range to detect outliers. It labels values outside the interval (L.Q.1.5 I.Q.R., U.Q.+1.5 I.Q.R.) as possible outliers. Values outside of (L.Q.3 I.Q.R., U.Q.+3 I.Q.R.) are labelled as probable outliers. In practice, the Minitab denitions correspond to roughly 2.7 S.D. and 4.7 S.D. respectively away from the mean. SKEWNESS Some data sets are roughly symmetrical but others show a tail to the right or, less often, to the left. These data sets are said to be skewed. Those that have a tail to the right are said to be Positively Skewed. The others are said to be Negatively Skewed. For positively skewed data, the Median will usually be smaller than the Mean and bigger than the Mode. The Trimmed Mean will usually be between the Median and the Mean. If the data are heavily skewed, the Median is a better measure of location than the Mean. Transformations If we calculate a new variable from an existing variable by taking the logarithms (logs) or the square root of the values, the new variable will have a dierent shape from the original variable. Both of these transformations tend to stretch out small values and to squash in large values. This reduces any positive skewness in the data and can make the distribution of the values more nearly symmetrical. Also, positive outliers may disappear and negative outliers may appear. The disadvantage of most transformations is that any dierences between groups on the transformed variable can be hard to interpret. This is not true for logs as the dierences on the log scale correspond to multiplicative factors on the original scale. Example: The dierence between the means of 2 groups after using a log10 transformation is 0.1. 100.1 = 1.259, so on the original scale, one group is 25.9% bigger than the other group. A table can contain summary statistics as well as counts. Example: The Minitab table below gives results in December 2001 for this module, split by the number of assessment web tests taken.

Rows: WebTests Score N 2 All Score Mean 36.000 44.810 68.167 65.212 Score StDev 11.489 14.559 16.407 18.133 Score Median 34.000 46.000 68.000 --
Note that the overall mean and standard deviation can be found from the group means and standard deviations. This cannot be done for medians. Care is needed with accuracy and weights.
Weighted Means The sample mean x = = =

i=1 n n i=1 n

1 xi i=1 n

wi x i

wi = 1
Thus an alternative view of the Mean is that it is a weighted sum of the observations, with all of the weights being the same. Sometimes it is desirable to use dierent weights in an average. Index numbers are just weighted means. Example: Retail Price Index. The weights are proportional to mean family expenditure on that item (obtained from O.N.S. household survey). Example: FTSE 100 index. The weights are proportional to market capitalisation (the weights are updated every 3 months).
To combine means, it is usually necessary to use weights which are proportional to sample sizes. Example: Mean age of 50 males = 22.6 years Mean age of 30 females = 19.4 years Mean age of combined group of 80 people = 50 22.6 + 30 19.22.6 + 19.4 = = 21.4
Example: Mean salary of 50 people = 18500 Mean salary of 30 males = 18100 Let mean salary of 20 females = x Then x+ 18100 = 50 0.4x = 7640 x = 19100 Frequency Tables If the data is provided as a table of frequencies, summary statistics can still be calculated. Each value in a class interval should be taken to be at the mid-point of the interval. Examples: Height class 1.50m 1.54m Interval is really 1.495m to 1.545m Mid-point is 1.52m Age class years Interval is really 15.0 to 19.997 Mid-point is 17.5 If fj is the observed frequency in class j and xj is the mid-point of class j, then in previous formulae: n= fj

n i=1 n i=1 Classes

Classes

fj xj fj x2 j

n n i=1 2
Sample Variance = (n1) x2 i n i=1
Example: Grouped Frequency Data - Handout 4 nn = 64

i=1 n i=1

xi = 111.78

x2 = 195.8556 i

Mean x = 111.78 = 1.747m Variance sx = 63 195.8556 111.78 = 0.So standard deviation sx = 0.009918 = 0.0996m Recoded data For the y data: y = s2 = 290 = 3.96726 y 64 sy = 3.96726 = 1.9918 Now x = 0.05y + 1.52 So for the x data: x = 0.+ 1.52 = 1.747m 64 sx = 0.05(1.9918) = 0.0996m EVENTS The descriptive methods used thus far are ne if we have measured all of the population of interest. If we have only measured a sample, we need to understand how the sampling process might aect our estimates. The sample estimates are likely to be close to the true population values, but how close? To answer this we need to study Probability. An experiment is any process where the result is not known in advance. In an experiment, we can distinguish between Events and Outcomes. The possible results of an experiment can be divided such that one and only one Outcome will occur. An Event is a collection of possible outcomes. Example: Experiment is to select a student. The outcome would be the student selected. The student is female is an event.

PROBABILITY The probability of an event is a measure of how likely it is to happen. It is measured on a scale from 0, which means never happens, to 1, which means always happens. P(Event E) = P(Outcome in E)
If there are n outcomes which are equally likely, then each outcome has probability If the event E occurs for r of these outcomes, then r P(E) = n number of favourable outcomes = number of possible outcomes Example: A trust has investments in 50 companies. Manufact UK Europe All 15 Retail 19 Other 16 All 50
Select a company at random. P(UK) = 28 = 0.P(Retail) = 19 = 0.P(UK And Retail) = 10 = 0.Example: Throw a fair die once. P(6) = 1 = 0.P(Even) = 3 = 0.Example: Throw 2 fair dice (1 red, 1 blue). There are 36 possible outcomes, all equally likely. 3 P(Sum is 4) = 36 = 0.outcomes give a sum of 4: (1,3) (2,2) (3,1). Note that (1,3) is not the same as (3,1).