Casio 229-Function User Guide - Page 2

Manufacturer:

CASIO

COMPUTER CO., LTD.

6-2, Hon-machi 1-chome

Shibuya-ku, Tokyo 151-8543, Japan

Responsible within the European Union:

CASIO EUROPE GmbH

Casio-Platz 1

22848 Norderstedt, Germany

This mark applies in EU countries only.

32

5

= 2

5

1

M

(

x

'

) 32

=

2.

To calculate

'

2

×

3

(= 3

'

2

= 4.242640687...) to three

decimal places (Fix 3)

N

1

(Fix)

3

1

2

*

3

=

4.243

To convert rectangular coordinates (

'

2

,

'

2

) to polar

coordinates

v

fx-82MS/85MS/300MS/350MS:

r

9

2

,

9

2

)

=

r

=

2.

~t

(F)

±

=

45.

• Press

~c

(E) to display the value of

r

, or

~t

(F) to

display the value of

±

.

fx-82SX PLUS/220 PLUS:

r

9

2

(

(,)

9

2

)

=

r

=

2.

!

q

(

y

,

±

)

=

±

=

45.

• Press

!

r

(

x

,

r

)

=

to display the value of

r

, or

!

q

(

y

,

±

)

=


±

.

To convert polar coordinates (

'

2

, 45°) to rectangular

coordinates

v


!

r

(Rec( )

9

2

,

45

=

x

=

1.

~t

(F)

y

=

1.

• Press

~c

(E) to display the value of

x

, or

~t

(F) to

display the value of

y

.


q

9

2

(

(,) 45

=

x

=

1.

!

q

(

y

,

±

)

=

y

=

1.

• Press

!

r

(

x

,

r

)

=


x

, or

!

q

(

y

,

±

)

=


y

.

(5 + 3) ! = 40320

(

5

+

3

)

1

E

(

x

!)

=

40320.

To obtain two random three-digit integers

1000

1

.

(Ran#)

=

459.

=

48.

(Actual results will differ.)

To generate random integers in the range of 1 to 6 (fx-82SX

PLUS/220 PLUS only)

1

2

(RanInt) 1

1

(

(,) 6

)=

2.

=

6.

(Actual results will differ.)

To determine the number of permutations and combinations

possible when selecting four people from a group of 10

Permutations:

10

1

{

(

n

P

r

) 4

=

5040.

Combinations:

10

{

4

=

210.

To perform the following calculations when Fix 3 is selected

for the number of display digits: 10 ÷ 3

×

3 and Rnd(10 ÷ 3)

×

3

N

1

(Fix)

3

10

/

3

*

3

=

10.000

10

/

3

=

1

0

(Rnd)

*

3

=

9.999

15.

Statistical Calculations (SD, REG*)

*fx-82MS/85MS/300MS/350MS only

To select this type of statistical

calculation:

(Regression formula

shown in parentheses)

Perform this key

operation:

Single-variable (X)

,

2

(SD)

Paired-variable (X, Y), linear

regression

(

y

= A + B

x

)

,

3

(REG)

1

(Lin)

Paired-variable (X, Y), logarithmic

regression

(

y

= A + Bln

x

)

,

3

(REG)

2

(Log)

Paired-variable (X, Y),

e

exponential regression

(

y

= A

e

B

x

)

,

3

(REG)

3

(Exp)

Paired-variable (X, Y), power

regression

(

y

= A

x

B

)

,

3

(REG)

e

1

(Pwr)

Paired-variable (X, Y), inverse

regression

(

y

= A + B/

x

)

,

3

(REG)

e

2

(Inv)

Paired-variable (X, Y), quadratic

regression

(

y

= A + B

x

+ C

x

2

)

,

3

(REG)

e

3

(Quad)

Inputting Data

• In the SD Mode and REG Mode, the

l

key operates as the

7

key.

• Always start data input with

!,

(CLR)

b

(Scl)

=

(

r

b

(Scl)

=

on the fx-82SX PLUS/220 PLUS) to clear statistical

memory.

• Input data using the key sequence shown below.

SD Mode: <

x

-data>

7

REG Mode: <

x

-data>

,

<

y

-data>

7

•

77

inputs the same data twice.

• You can also input multiple entries of the same data using

!

,

(;)

(

!

)

(;) on the fx-82SX PLUS/220 PLUS).

k

8

8

9

9

10

10

11

11

12

12

13

13

Data Input Precautions

• While inputting data or after inputting data is complete, you can use

the

f

and

c

keys to scroll through data you have input. If you

input multiple entries of the same data using

!

,

(;) (

!

)

(;) on

the fx-82SX PLUS/220 PLUS) to specify the data frequency (number

of data items) as described above, scrolling through data shows

both the data item and a separate screen for the data frequency

(Freq).

• Input the new value and then press the

=

key to replace the old

value with the new one. This also means that if you want to perform

some other operation, you should always press the

A

key first to

exit data display.

• Pressing the

7

key instead of

=

after changing a value on the

display registers the value you input as a new data item, and leaves

the old value as it is.

• You can delete a data value displayed using

f

and

c

by pressing

!

l

(CL). Deleting a data value causes all values following it to

be shifted up.

• The message “Data Full” appears and you will not be able to input

any more data if there is no memory left for data storage. If this

happens, press the

=

key to display the screen shown below.

Press

c

to exit data input without registering

the value you just input.

Press

b

if you want to register the value

you just input. If you do this, however, you will not be able to display

or edit any of the data you have input.

• After inputting statistical data in the SD Mode or REG Mode, you

will be unable to display or edit individual data items any longer

after perform either the following operations: changing to another

mode; changing the regression type.

• Entering the REG Mode and selecting a regression type (Lin, Log,

Exp, Pwr, Inv, Quad) clear variables A through F, X, and Y.

• Do not use variables A through F, X, or Y to store data when

performing statistical calculations.

Obtaining Statistical Values from Input Data

Supported statistical variables and the keys you should press to recall

them are shown below.


Sum:

Σ

x

2

,

Σ

x

,

Number of Items:

n

,

Mean:

o

,

Population Standard

Deviation:

σ

x

,

Sample Standard Deviation:

s

x

!

e

to

j


For single-variable statistical calculations, the variables marked with

an asterisk (*) are available.

Sum:

Σ

x

2

*,

Σ

x

*,

Σ

y

2

,

Σ

y

,

Σ

xy

,

Σ

x

3

,

Σ

x

2

y

,

Σ

x

4

,

Number of Items:

n

*

Σ

x

2

,

Σ

x

,

n

...........

!

b

(S-SUM)

b

to

d

Σ

y

2

,

Σ

y

,

Σ

xy

........

!

b

(S-SUM)

e

b

to

d

Σ

x

3

,

Σ

x

2

y

,

Σ

x

4

.....

!

b

(S-SUM)

ee

b

to

d

(Quadratic

Regression only)

Mean:

o

*,

p

,

Population Standard Deviation:

σ

x

*,

σ

y

,

Sample

Standard Deviation:

s

x

*, s

y

o

,

σ

x

, s

x

..............

!

c

(S-VAR)

b

to

d

p

,

σ

y

, s

y

...............

!

c

(S-VAR)

e

b

to

d

Regression Coefficients:

A, B,

Correlation Coefficient:

r

Regression Coefficients for Quadratic Regression:

A, B, C

!

c

(S-VAR)

ee

b

to

d

Estimated Values:

m

,

n

Estimated Values for Quadratic Regression:

m

1

,

m

2

,

n

!

c

(S-VAR)

eee

b

to

c

(or

d

)

•

m

,

m

1

,

m

2

and

n

are not variables. They are commands of the type

that take an argument immediately before them. See “Calculating

Estimated Values” for more information.

To calculate the mean (

o

) and population standard

deviation (

σ

x

) for the following data: 55, 54, 51, 55, 53, 53,

54, 52

,

c

(SD)

55

7

54

7

51

7

55

7

53

77

54

7

52

7


!

h

(

o

)

=

53.375

!

i

(

σ

x

)

=

1.316956719


!

c

(S-VAR)

b

(

o

)

53.375

!

c

(S-VAR)

c

(

σ

x

)

1.316956719

2


To calculate the linear

regression and logarithmic regression correlation

coefficients (

r

) for the following paired-variable data

and determine the regression formula for the strongest

correlation: (

x

,

y

) = (20, 3150), (110, 7310), (200, 8800),

(290, 9310). Specify Fix 3 (three decimal places) for results.

,

3

(REG)

1

(Lin)

,

1

(Fix)

3

20

,

3150

7

110

,

7310

7

200

,

8800

7

290

,

9310

7

!

2

(S-VAR)

ee

3

(r)

=

0.923

,

3

(REG)

2

(Log)

20

,

3150

7

110

,

7310

7

200

,

8800

7

290

,

9310

7

!

2

(S-VAR)

ee

3

(r)

=

0.998

!

2

(S-VAR)

ee

1

(A)

=

−3857.984

!

2

(S-VAR)

ee

2

(B)

=

2357.532

Logarithmic Regression Formula:

y

= –3857.984 + 2357.532ln

x

k

k

1

1

Calculating Estimated Values

Based on the regression formula obtained by paired-variable

statistical calculation, the estimated value of

y

can be calculated for

a given

x

-value. The corresponding

x

-value (two values,

x

1

and

x

2

, in

the case of quadratic regression) also can be calculated for a value

of

y

in the regression formula.

To determine the estimate value for

y

when

x

= 160 in the

regression formula produced by logarithmic regression of

the data in

2

. Specify Fix 3 for the result. (Perform the

following operation after completing the operations in

2

.)

160

1

2

(S-VAR)

eee

2

(

n

)

=

8106.898

Important:

Regression coefficient, correlation coefficient, and

estimated value calculations can take considerable time when there

are a large number of data items.

16.

Calculation Ranges, Number of

Digits, and Precision

Calculation Range and Precision

Calculation Range:

±1

×

10

–99

to 9.999999999

×

10

99

or 0

Number of Digits for Internal Calculation:

15 digits

Precision:

In general, ±1 at the 10th digit for a single calculation.

Precision for exponential display is ±1 at the least significant digit.

Errors are cumulative in the case of consecutive calculations.

Function Calculation Input Ranges and Precision

Functions

Input Range

sin

x

cos

x

DEG

0

´

|

x

|

³

9

×

10

9

RAD

0

´

|

x

|

³

157079632.7

GRA

0

´

|

x

|

³

1

×

10

10

tan

x

DEG

Same as sin

x

, except when

|

x

|

= (2

n

–1)

×

90.

RAD

Same as sin

x

, except when

|

x

|

= (2

n

–1)

× π

/2.

GRA

Same as sin

x

, except when

|

x

|

= (2

n

–1)

×

100.

sin

–1

x

cos

–1

x

0

´

|

x

|

´

1

tan

–1

x

0

´

|

x

|

´

9.999999999

×

10

99

sinh

x

cosh

x

0

´

|

x

|

´

230.2585092

sinh

–1

x

0

´

|

x

|

´

4.999999999

×

10

99

cosh

–1

x

1

´

x

´

4.999999999

×

10

99

tanh

x

0

´

|

x

|

´

9.999999999

×

10

99

tanh

–1

x

0

´

|

x

|

´

9.999999999

×

10

–1

log

x

/ln

x

0

³

x

´

9.999999999

×

10

99

10

x

–9.999999999

×

10

99

´

x

´

99.99999999

e

x

–9.999999999

×

10

99

´

x

´

230.2585092

'

x

0

´

x

³

1

×

10

100

x

2

|

x

|

³

1

×

10

50

x

–1

|

x

|

³

1

×

10

100

;

x

G

0

3

'

x

|

x

|

³

1

×

10

100

x

!

0

´

x

´

69 (

x

is an integer)

n

P

r

0

´

n

³

1

×

10

10

, 0

´

r

´

n

(

n

,

r

are integers)

1

´

{

n

!/(

n

–

r

)!}

³

1

×

10

100

n

C

r

0

´

n

³

1

×

10

10

, 0

´

r

´

n

(

n

,

r

are integers)

1

´

n

!/

r

!

³

1

×

10

100

or 1

´

n

!/(

n

–

r

)!

³

1

×

10

100

Pol(

x

,

y

)

|

x

|

,

|

y

|

´

9.999999999

×

10

99

x

2

+

y

2

´

9.999999999

×

10

99

Rec(

r

,

±

)

0

´

r

´

9.999999999

×

10

99

±

: Same as sin

x

°’ ”

|

a

|

,

b

,

c

³

1

×

10

100

; 0

´

b

,

c

The display seconds value is subject to an error of

±1 at the second decimal place.

|

x

|

³

1

×

10

100

Decimal

↔

Sexagesimal Conversions

0°0´0˝

´

|

x

|

´

9999999°59´

x

y

x

±

0: –1

×

10

100

³

y

log

x

³

100

x

= 0:

y

±

0

x

³

0:

y

=

n

,

1

2

n

+1

(

n

is an integer)

However: –1

×

10

100

³

y

log

|

x

|

³

100

x

'

y

y

±

0:

x

G

0, –1

×

10

100

³

1/

x

log

y

³

100

y

= 0:

x

±

0

y

³

0:

x

= 2

n

+1,

1

n

(

n

G

0;

n

is an integer)

However: –1

×

10

100

³

1/

x

log

|

y

|

³

100

a

b

/

c

Total of integer, numerator, and denominator must

be 10 digits or less (including division marks).

RanInt#(

a

,

b

)

a

³

b

;

|

a

|

,

|

b

|

³

1

×

10

10

;

b

–

a

³

1

×

10

10

(

a

,

b

are

integers)

k

k

k

3

3

• Precision is basically the same as that described under “Calculation

Range and Precision”, above.

• Calculations that use any of the functions or settings shown below

require consecutive internal calculations to be performed, which can

cause accumulation of error that occurs with each calculation.

x

y

,

x

'

y

,

3

'

,

x

!,

n

P

r

,

n

C

r

; °,

r

,

g

(angle unit: radians);

σ

x

, s

x

, regression

coefficient.

• Error is cumulative and tends to be large in the vicinity of a function’s

singular point and inflection point.

• Accumulation of errors tends to occur during statistical calculations

involving data in which there is a large number of decimal places

and there is little difference between data items. Input of statistical

data is limited to six decimal places.

17.

Error Messages

The calculator will display an error message whenever an error occurs

for any reason during a calculation.

• Press

d

or

e

to return to the calculation screen. The cursor will

be positioned at the location where the error occurred, ready for

input. Make the necessary corrections to the calculation and execute

it again. (Not included on the fx-82SX PLUS)

• Press

A

to return to the calculation screen. Note that this also

clears the calculation that contained the error.

Math ERROR

Cause:

• The intermediate or final result of the calculation you

are performing exceeds the allowable calculation range.

• Your

input exceeds the allowable input range.

• The calculation you are

performing contains an illegal mathematical operation (such as

division by zero).

Action:

• Check the input values and reduce the number of digits.

• When using independent memory or a variable as the argument of

a function, make sure that the memory or variable value is within the

allowable range for the function.

Stack ERROR

Cause:

The calculation you are performing has caused the capacity

of the numeric stack or the command stack to be exceeded.

Action:

• Simplify the calculation expression.

• Try splitting the

calculation into two or more parts.

Syntax ERROR

Cause:

There is a problem with the format of the calculation you

are performing.

Action:

Make necessary corrections.

Arg ERROR

Cause:

Improper use of an argument.

Action:

Make necessary corrections.

18.

Before Assuming Malfunction of the

Calculator...

Perform the following steps whenever an error occurs during a

calculation or when calculation results are not what you expected.

Note that you should make separate copies of important data before

performing these steps.

1. Check the calculation expression to make sure that it does not

contain any errors.

2. Make sure that you are using the correct mode for the type of

calculation you are trying to perform.

3. If the above steps do not correct your problem, press the

O

key.

4. Initialize all modes and settings. See “Initializing Calculator

Settings”.

19.

Replacing the Battery

Important:

Removing the battery will cause all of the calculator’s

memory contents to be deleted.

1. Press

1A

(OFF) to turn off the calculator.

• To ensure that you do not accidentally turn on power while

replacing the battery, slide the hard case onto the front of the

calculator (fx-350MS).

2. Remove the cover as shown in the illustration and replace the

battery, taking care that its plus (+) and minus (–) ends are facing

correctly.

Screw

Screw

Screw

Screw

Screw

fx-82MS/82SX PLUS/

220 PLUS

fx-350MS

fx-85MS/300MS

3. Replace the cover.

4. Initialize the calculator. See “3. Initializing the Calculator”.

• Do not skip the above step!

20.

Specifications

Power Requirements:

fx-82MS/82SX PLUS/220 PLUS: AA-size battery R6P (SUM-3)

×

1

fx-350MS: Button battery LR44 (GPA76)

×

1

fx-85MS/300MS: Built-in solar cell; button battery LR44 (GPA76)

×

1

Approximate Battery Life:

fx-82MS/82SX PLUS/220 PLUS: 17,000 hours (continuous display

of flashing cursor)

fx-350MS: 9,000 hours (continuous operation)

fx-85MS/300MS: 3 years (based on one hour of operation per day)

Power Consumption:

0.0001 W (fx-82MS/82SX PLUS/220 PLUS/350MS)

Operating Temperature:

0°C to 40°C (32°F to 104°F)

Dimensions

(H

×

W

×

D)/

Approximate Weight

(including the battery)

fx-82MS

18.6

×

85

×

156 mm

3

/

4

±

×

3

3

/

8

±

×

6

1

/

8

±

115 g

(4.1 oz)

fx-82SX PLUS

fx-220 PLUS

19.5

×

78

×

155 mm

3

/

4

±

×

3

1

/

8

±

×

6

1

/

8

±

115 g

(4.1 oz)

fx-85MS

fx-300MS

fx-350MS

12.2

×

85

×

155 mm

1

/

2

±

×

3

3

/

8

±

×

6

1

/

8

±

100 g

(3.5 oz)

RJA521989-001V01

Casio 229-Function User Guide - Page 2

Function Calculation Input Ranges and Precision - calculator functions

Page 2 highlights