Citizen SR-281N: инструкция
Раздел: Электроника
Тип: Калькулятор
Инструкция к Калькулятору Citizen SR-281N
File name : CBM_SR-281N_IB_English_black_v09330.doc
Date: 2009/3/30 Trimmed Size : 140 x 75 mm SCALE 1 : 1
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General Guide.............................................................................................2
Turning on or off .......................................................................................2
Battery replacement .................................................................................2
Auto power-off function.............................................................................2
Reset operation ........................................................................................2
Contrast adjustment .................................................................................2
Display readout.........................................................................................3
Before Starting Calculation........................................................................3
Using " MODE " keys................................................................................3
Using " 2nd " Keys....................................................................................4
Corrections ...............................................................................................4
Undo function ...........................................................................................4
Replay function.........................................................................................5
Memory calculation...................................................................................5
Order of operations...................................................................................6
Accuracy and Capacity .............................................................................7
Error conditions ........................................................................................9
Basic Calculations......................................................................................9
Arithmetic calculation................................................................................9
Parentheses calculations........................................................................10
Percentage calculation ........................................................................... 11
Display notations .................................................................................... 11
Scientific Functional Calculations ..........................................................13
Logarithms and Antilogarithms ...............................................................13
Fraction calculation.................................................................................13
Angle unit conversions............................................................................14
Sexagesimal
↔
Decimal transformation.................................................15
Trigonometric / Inverse-Tri. functions......................................................15
Hyperbolic / Inverse-Hyp. functions ........................................................16
Coordinates transformation ....................................................................16
Probability...............................................................................................17
Other functions ( 1/x,
,
3
,
X
, x
2
, x
3
, x
y
, INT, FRAC ) ................18
Unit Conversion ......................................................................................19
Physics constants ...................................................................................19
Base–n calculations .................................................................................24
Bases conversions..................................................................................25
Block Function ........................................................................................25
Basic arithmetic operations for bases .....................................................26
Negative expressions .............................................................................26
Logical operation ....................................................................................27
Statistical Calculations ............................................................................27
Entering data ..........................................................................................27
Displaying results....................................................................................28
Deleting data ..........................................................................................31
Editing data ............................................................................................31
FULL message .......................................................................................32
Complex Calculations ..............................................................................32
Contents
File name : CBM_SR-281N_IB_English_black_v09330.doc
Date: 2009/3/30 Trimmed Size : 140 x 75 mm SCALE 1 : 1
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General
Guide
Turning on or off
To turn the calculator on, press [ ON/C ] ; To turn the calculator off,
press [ 2nd ] [ OFF ].
Battery replacement
The calculator is powered by two alkaline batteries (G13 or LR44).
When the display dims, replace the batteries. Be careful not to be
injured when you replace the battery.
1. Unscrew the screws on the back of the calculator.
2. Insert a flat bladed screwdriver into the slot between the upper and
lower case then carefully twist it to separate the case.
3. Remove both batteries and dispose of them properly. Never allow
children to play with batteries.
4. Wipe off the new batteries with a dry cloth to maintain good contact.
5. Insert the two new batteries with their flat sides (plus terminals) up.
6. Align the upper and lower cases then snap them to close together.
7. Tighten the screws.
Auto power-off function
This calculator automatically turns it off when not operated for
approximately 6~9 minutes. It can be reactivated by pressing [ ON/C ]
key and the display, memory, settings are retained.
Reset operation
If the calculator is on but you get unexpected results, press [ MODE ]
[ 4 ] ( RESET ) in sequence. A message appears on the display to
confirm whether you want to reset the calculator and clear memory
contents.
RESET : N Y
Move the cursor to " Y " by [
], then press [=] to clear all variables,
pending operations, statistical data, answers, all previous entries, and
memory; To cancel the reset operation without clearing the calculator,
please choose " N ".
If the calculator is lock and further key operations becomes impossible,
please use a pointed object to press the reset hole to release the
condition. It will return all settings to default settings.
Contrast adjustment
Pressing the [ – ] or [ + ] following [ MODE ] key can make the contrast
of the screen lighter or darker. Holding either key down will make the
display become respectively lighter or darker.
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Display readout
The display comprises two lines and indicators. The upper line is a dot
display up to 128 characters. The lower line is capable of displaying a
result of up to 12 digits, as well as 2-digits positive or negative
exponent.
When formulas are input and executed the calculation by [=], they are
displayed on the upper line, and then results are shown on the lower
line.
The following indictors appear on the display to indicate you the
current status of the calculator.
Indicator Meaning
M Running
memory
–
Result is negative
E Error
STO
Storing variable mode is active
RCL
Recalling variable mode is active
2nd
2nd set of function keys are active
HYP
Hyperbolic-trig function will be calculated
ENG
Engineering symbol notation
CPLX
Complex number mode is active
CONST
Display physics constants
DEGRAD
Angle mode : DEGrees, GRADs, or RADs
BIN Binary
base
OCT Octal
base
HEX Hexadecimal
base
( )
Open parentheses
TAB
Number of decimal places displayed is fixed
STAT
Statistics mode is active
REG
Regression mode is active
EDIT
Statistics data is being edited
CPK
CPK : Process capability
CP : Precision capability
USL
Set upper specification limit
LSL
Setting lower specification limit
i Imaginary
part
Allow to use undo function
Before Starting Calculation
Using " MODE " keys
Press [ MODE ] to display mode menus when specifying an operating
mode ( " 1 MAIN ", " 2 STAT ", " 3 CPLX ", " 4 RESET " ) or the
engineering symbol notation ( " 5 ENG " ).
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1 MAIN : Use this mode for basic calculations, including scientific
calculations and Base–n calculations.
2 STAT : Use this mode to perform single–variable and
paired–variable statistical calculations and regression
calculations.
3 CPLX : Use this mode to perform complex number calculation.
4 RESET : Use this mode to perform reset operation.
5 ENG : Use this mode to allow engineering calculations utilizing
engineering symbol.
Give " 2 STAT " as an example :
Method 1 : Press [ MODE ] and then scroll through the menus using
[
] or [ 2nd ] [
] until " 2 STAT " is underlined,
then enter the desired mode by pressing [=].
Method 2 : Press [ MODE ] and then key in directly the number of
the mode, [ 2 ] , to enter the desired mode immediately.
Using " 2nd " Keys
When you press [ 2nd ], the " 2nd " indicator shown in the display is to
tell you that you will be selecting the second function of the next key
you press. If you press [ 2nd ] by mistake, simply press [ 2nd ] again to
remove the " 2nd " indicator.
Corrections
If you have made a mistake when entering a number (but you have not
yet pressed an arithmetic operator key), just press [ CE ] to clear the
last entry then input it again, or delete individual digits by the
backspace key [
], or clear all entry by [ ON/C ].
After making corrections, input of the formula is complete, the answer
can be obtained by pressing [=]. You can also press [ ON/C ] to clear
the immediate results completely (except clearing memory). If you
press the wrong arithmetic operation key, just press the correct key to
replace it.
Undo function
The unit offers an undo function which allows you to undo some of the
errors you just have made.
When a character which is just deleted by [
], an entry which is just
cleared [ CE ], or which is just cleared by [ ON/C ], the "
" indicator
shown in the display is to tell you that you can press [ 2nd ] [
] to
cancel the operation.
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Replay function
This function stores operations that just have been executed. After
execution is completed, pressing [
] or [ 2nd ] [
] key will
display the operation executed. Pressing [
] will display the
operation from the beginning, with the cursor located under the first
character. Pressing [ 2nd ] [
] will display the operation from the
end, with the cursor located at the space following the last character.
You can continue moving the cursor by [
] or [ 2nd ] [
] and
editing values or commands for subsequent execution.
Memory calculation
Memory variable
The calculator has nine memory variables for repeated use -- A, B, C,
D, E, F, M, X, Y. You can store a real number in any of the nine
memory variables.
•
[ STO ] + [ A ] ~ [ F ], [ M ], [ X ] ~ [ Y ] lets you store values to
variables.
•
[ RCL ] + [ A ] ~ [ F ], [ M ], [ X ] ~ [ Y ] recalls the value of the
variable.
•
[ 0 ] [ STO ] + [ A ] ~ [ F ], [ M ], [ X ] ~ [ Y ] clears the content to a
specified memory variable.
¾
(1) Put the value 30 into variable A
DEG
3 0
Æ
A
30 [ STO ] [ A ]
3 0
.
¾
(2) Multiple 5 to variable A, then put the result into variable B
DEG
5
¼
A =
5 [ x ] [ RCL ] [ A ] [=]
1 5 0
.
DEG
1 5 0
Æ
B
[ STO ] [ B ]
1 5 0
.
¾
(3) Clear the value of variable B
DEG
0
Æ
B
0 [ STO ] [ B ]
0
.
DEG
B =
[ RCL ] [ B ] [=]
0
.
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Running memory
You should keep the following rules in mind when using running
memory.
• Press [ M+ ] to add a result to running memory and the " M "
indicator appears when a number is stored in the memory. Press
[ MR ] to recall the content of running memory.
• Recalling from running memory by pressing [ MR ] key does not
affect its contents .
• Running memory is not available when you are in statistics mode.
• The memory variable M and running memory utilize the same
memory area.
• In order to replace the content of the memory with the displayed
number, please press [ X M ] key.
• To clear the content of running memory, you can press [ 0 ] [ X M ],
[ ON/C ] [ X M ] or [ 0 ] [ STO ] [ M ] in sequence.
¾
[ ( 3 x 5 ) + ( 56 7 ) + ( 74 – 8 x 7 ) ] = 41
DEG
0 [ X M ]
0
.
DEG
7 4 – 8
¼
7 M +
3 [ x ] 5 [ M+ ] 56 [ ] 7 [ M+ ] 74
[ – ] 8 [ x ] 7 [ M+ ]
M
1 8
.
DEG
M
[ MR ]
M
4 1
.
DEG
0 [ X M ]
0
.
(Note) : Besides pressing [ STO ] or [ X M ] key to store a value, you
can also assign values to memory variable M by [ M+ ].
However, when [ STO ] [ M ] or [ X M ] is used, previous
memory contents stored in variable M are cleared and
replaced it with the newly assigned value. When [ M+ ] is used,
values is added to present sum in memory.
Order of operations
Each calculation is performed in the following order of precedence:
1) Fractions
2) Expression inside parentheses.
3) Coordinates transformation ( P R , R P )
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4) Type A functions which are required entering values before
pressing the function key, for example, x
2
,1/x,
π
, x!, %, RND,
ENG,
,
, x ', y ' .
5) x
y
,
X
6) Type B functions which are required pressing the function key
before entering, for example, sin, cos, tan, sin
–1
, cos
–1
, tan
–1
,
sinh, cosh, tanh, sinh
–1
, cosh
–1
, tanh
–1
, log, ln, FRAC, INT,
√
,
3
, 10
X
, e
X
, NOT, EXP, DATA in STAT mode.
7) +/–, NEG
8) nPr,
nCr
9) x
,
10) +, –
11) AND, NAND –-- only Base–n mode
12) OR, XOR, XNOR --- only Base–n mode
Accuracy and Capacity
Output digits : Up to 12 digits.
Calculating digits : Up to 14 digits
In general, every reasonable calculation is displayed up to 12 digits
mantissa, or 12-digits mantissa plus 2-digits exponent up to 10
± 99
.
Numbers used as input must be within the range of the given function
as follow :
Functions
Input range
sin x
cos x
tan x
Deg :
x
<
4.5 x 10
10
deg
Rad :
x
<
2.5 x 10
8
π
rad
Grad :
x
<
5 x 10
10
grad
however, for tan x
Deg :
x
≠
90 (2n+1)
Rad :
x
≠
2
π
(2n+1)
Grad :
x
≠
100 (2n+1), (n is an integer)
sin
–1
x, cos
–1
x
x
≦
1
tan
–1
x
x
<
1 x 10
100
sinh x, cosh x
x
≦
230.2585092
tanh x
x
<
1 x 10
100
sinh
–1
x
x
<
5 x 10
99
cosh
–1
x
1
≦
x
<
5 x 10
99
File name : CBM_SR-281N_IB_English_black_v09330.doc
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tanh
–1
x
x
<
1
log x, ln x
1 x 10
–99
≦
x
<
1 x 10
100
10
x
–1 x 10
100
<
x
<
100
e
x
–1 x 10
100
<
x
≦
230.2585092
x
0
≦
x
<
1 x 10
100
x
2
x
<
1 x 10
50
x
3
x
<
2.15443469003 x 10
33
1/x
x
<
1 x 10
100
, x
≠
0
3
x
x
<
1 x 10
100
x !
0
≦
x
≦
69, x is an integer.
R P
2
2
y
+
x
<
1 x 10
100
P R
0
≦
r
<
1 x 10
100
Deg
：
│
θ
│
<
4.5 x 10
10
deg
Rad
：
│
θ
│
<
2.5 x 10
8
π
rad
Grad
：
│
θ
│
<
5 x 10
10
grad
however, for tan x
Deg
：
│
θ
│
≠
90 (2n+1)
Rad
：
│
θ
│
≠
2
π
(2n+1)
Grad
：
│
θ
│
≠
100 (2n+1), (n is an integer)
│
D
│
, M, S
<
1 x 10
100
, 0
≦
M, S
x
<
1 x 10
100
x
y
x
>
0 : –1 x 10
100
<
y log x
<
100
x = 0 : y
>
0
x
<
0 : y = n, 1/(2n+1), n is an integer.
but –1 x 10
100
<
y log
│
x
│
<
100
x
y
y
>
0 : x
≠
0, –1 x 10
100
<
x
1
log y
<
100
y = 0 : x
>
0
y
<
0 : x=2n+1, l/n, n is an integer.(n
≠
0)
but –1 x 10
100
<
x
1
log
│
y
│
<
100
a b/c
Input
：
Total of integer, numerator and
denominator must be within 12 digits
(includes division marks)
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Result
：
Result displayed as fraction for
integer when integer, numerator and
denominator are less than 1 x 10
12
nPr, nCr
0
≦
r
≦
n, n
≦
10
100
, n,r are integers.
STAT
x
<
1 x 10
50
,
y
<
1 x 10
50
σ
x,
σ
y,
x
, y ,a, b, r : n
≠
0 ;
Sx, Sy
：
n
≠
0, 1 ; x
n
= 50 ; y
n
= 50 ;
Number of repeats
≤
255, n is an integer.
DEC
– 2147483648
≦
x
≦
2147483647
BIN
0
≦
x
≦
01111111111111111111111111111111
(for zero or positive)
10000000000000000000000000000000
≦
x
≦
11111111111111111111111111111111
(for negative)
OCT
0
≦
x
≦
17777777777 (for zero or positive)
20000000000
≦
x
≦
37777777777
(for negative)
HEX
0
≦
x
≦
7FFFFFFF ( for zero or positive)
80000000
≦
x
≦
FFFFFFFF (for negative)
Error conditions
Error message “
E
” will appear on the display and further calculation
becomes impossible when any of the following condition occur.
1) You attempted to divide by 0
2) When allowable input range of function calculations exceeds the
range specified
3) When result of function calculations exceeds the range specified
4) When the [ ( ] key is used more than 13 levels in a single
expression
5) When
USL
<
LSL value
To release the above errors, please press [ ON/C ].
Basic
Calculations
Use MAIN ( [ MODE ] 1 ( MAIN ) ) mode for basic calculations.
Arithmetic calculation
Arithmetic operations are performed by pressing the keys in the same
sequence as in the expression.
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¾
7 + 5 x 4 = 27
DEG
7 + 5
¼
4 =
7 [ + ] 5 [ x ] 4 [=]
2 7
.
For negative values, press [ +/– ] after entering the value; You can
enter a number in mantissa and exponent form by [ EXP ] key.
¾
2.75 x 10
– 5
= 0.0000275
DEG
2
.
7 5 E – 0 5 =
2.75 [ EXP ] 5 [ +/– ] [=]
0
.
0 0 0 0 2
7 5
Results greater than 10
12
or less than 10
–11
are displayed in
exponential form.
¾
12369 x 7532 x 74010 = 6895016425080
= 6.89501642508 x 10
12
DEG
1 2 3 6 9
¼
7 5 3 2
¼
7
12369 [ x ] 7532 [ x ] 74010
[=]
6
.
8 9 5 0 1 6 4 2 5 0 8
12
Parentheses calculations
Operations inside parentheses are always executed first.
SR-281N
can use up to 13 levels of consecutive parentheses in a single
calculation.
Closed parentheses occurring immediately before operation of the [ ) ]
key may be omitted, no matter how many are required.
¾
2 x { 7 + 6 x ( 5 + 4 ) } = 122
DEG
2
¼
( 7 + 6
¼
( 5 + 4 =
2 [ ( ] 7 [ + ] 6 [ ( ] 5 [ + ] 4 [=]
1 2 2
.
(Note) : A multiplication sign "
x
" occurring immediately before an
open parenthesis can be omitted.
The correct result cannot be derived by entering [ ( ] 2 [ + ] 3 [ ) ] [ EXP ]
2. Be sure to enter [ x ] between the [ ) ] and [ EXP ] in the below
example.
¾
( 2 + 3 ) x 10
2
= 500
DEG
( 2 + 3 )
¼
1 E 0 2 =
[ ( ] 2 [ + ] 3 [ ) ] [ x ] [ EXP ] 2
[=]
5
0 0
.
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Percentage calculation
[ 2nd ] [ % ] divides the number in the display by 100. You can use this
key sequence to calculate percentages, add-ons, discounts, and
percentage ratios.
¾
120 x 30 % = 36
DEG
1 2 0
¼
3 0 % =
120 [ x ] 30 [ 2nd ] [ % ] [=]
3 6
.
¾
88 55 % = 160
DEG
8 8
5 5 % =
88 [ ] 55 [ 2nd ] [ % ] [=]
1 6 0
.
Display notations
The calculator has the following display notations for the display value.
Fixed-point / Floating Notations
To specify the number of decimal places, press [ 2nd ] [ TAB ] and
then a value indicating the number of places ( 0~9 ). Values are
displayed rounded off to the place specified. To return floating setting,
press [ 2nd ] [ TAB ] [ • ].
Scientific Notation
To change the display mode between floating and scientific notation,
press [ F
↔
E ].
Engineering Notation
Pressing [ ENG ] or [ 2nd ] [
] will cause the exponent display for
the number being displayed to change in multiples of 3.
¾
6 7 = 0.85714285714…
DEG
6
7 =
6 [ ] 7 [=]
0
.
8 5 7 1 4 2 8 5 7 1 4
DEG
TAB
6
7 =
[ 2nd ] [ TAB ] 4
0
.
8 5 7 1
DEG
TAB
6
7 =
[ 2nd ] [ TAB ] 2
0
.
8 6
DEG
6
7 =
[ 2nd ] [ TAB ] [ • ]
0
.
8 5 7 1 4 2 8 5 7 1 4
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DEG
6
7 =
[ F
↔
E ]
8
.
5 7 1 4 2 8 5 7 1 4 3
–01
DEG
[ ENG ]
8 5 7
.
1 4 2 8 5 7 1 4 3
–03
DEG
[ 2nd ] [
] [ 2nd ] [
]
0
.
0 0 0 8 5 7 1 4 2 8 5
03
Engineering Symbol Notation
Each time you specify the ENG mode, a displayed result is
automatically shown with the corresponding engineering symbol.
Y
yotta
= 10
24
,
Z
zetta
= 10
21
,
E
exa
= 10
18
,
P
peta
= 10
15
,
T
tera
= 10
12
,
G
giga
= 10
9
,
M
mega
= 10
6
,
K
kilo
= 10
3
,
m
milli
= 10
– 3
,
μ
micro
= 10
– 6
,
n
nano
= 10
– 9
,
p
pico
= 10
– 12
,
f
femto
= 10
– 15
,
a
atto
= 10
– 18
,
z
zepto
= 10
– 21
,
y
yocto
= 10
– 24
Perform the following operation to specify engineering symbol
notation.
[ MODE ] 5 ( ENG )
To exit from this mode, press [ MODE ] 5 once again.
¾
6 7 = 0.85714285714…
ENG
DEG
[ MODE ] 5
0
.
ENG
DEG
6
7 =
m
6 [ ] 7 [=]
8
5
7
.
1 4 2 8 5 7 1
4 3
ENG
DEG
μ
[ ENG ]
8 5 7 1 4 2
.
8 5 7 1 4 3
ENG
DEG
K
[ 2nd ] [
] [ 2nd ] [
] [ 2nd ]
[
]
0
.
0 0 0 8 5 7 1 4 2 8 5
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Scientific Functional Calculations
Use MAIN ( [ MODE ] 1 ( MAIN ) ) mode for scientific function
calculations.
Logarithms and Antilogarithms
The calculator can calculate common and natural logarithms and
anti-logarithms using [ log ], [ ln ], [ 2nd ] [ 10
x
], and [ 2nd ] [ e
x
].
¾
ln 7 + log 100 = 3.94591014906
DEG
l n 7 + l o g 1 0 0 =
[ ln ] 7 [ + ] [ log ] 100 [=]
3
.
9 4 5 9 1 0 1 4 9 0 6
¾
10
2
+ e
–5
= 100.006737947
DEG
10
^ 2 + e ^ – 5 =
[ 2nd ] [ 10
X
] 2 [ + ] [ 2nd ] [ e
X
] 5
[ + / – ] [=]
1 0 0
.
0 0 6 7 3 7 9 4 7
Fraction calculation
Fraction value display is as follow :
5
」
12 Display of
12
5
56
∪
5
」
12 Display of 56
12
5
(Note): Values are automatically displayed in decimal format whenever
the total number of digits of a fractional values ( integer +
numerator + denominator + separator marks ) exceeds 12.
To enter a mixed number, enter the integer part, press [ a b/c ], enter
the numerator, press [ a b/c ], and enter the denominator ; To enter an
improper fraction, enter the numerator, press [ a b/c ], and enter the
denominator.
¾
21
8
22
7
5
14
3
2
7
=
+
DEG
7
2
3
+ 1 4
5
7
7 [ a b/c ] 2 [ a b/c ] 3 [ + ] 14 [ a b/c ]
5 [ a b/c ] 7 [=]
2 2
8
2 1
.
During a fraction calculation, if the figure is reducible, a figure is
reduced to the lowest terms after pressing a function command key
( [ + ], [ – ], [ x ] or [ ] ) or the [=] key. By pressing [ 2nd ] [
d/e ], the
displayed value will be converted to the improper fraction and vice
versa. To convert between a decimal and fractional result, press
[ a b/c ].
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-E14-
¾
2
9
5
.
4
2
1
4
4
2
4
=
=
=
DEG
4
2
4
=
4 [ a b/c ] 2 [ a b/c ] 4 [=]
4
1
2
.
DEG
4
2
4
=
[ a b/c ]
4
.
5
DEG
4
2
4
=
[ a b/c ] [ 2nd ] [ d/e ]
9
2
.
DEG
4
2
4
=
[ 2nd ] [
d/e ]
4
1
2
.
Calculations containing both fractions and decimals are calculated in
decimal format.
¾
55
.
12
75
.
3
5
4
8
=
+
DEG
8
4
5
+ 3
.
7 5 =
8 [ a b/c ] 4 [ a b/c ] 5 [ + ] 3.75
[=]
1 2
.
5 5
Angle unit conversions
The calculator enables you to convert an angle unit among
degrees(DEG), radians(RAD), and grads(GRAD).
The relation among the three angle units is :
180
°
=
π
rad = 200 grad
1) To change the default setting to another setting, first press [ 2nd ]
[ DRG ] key repeatedly until the angle unit you want is indicated in
the display.
2) After entering a value, press [ 2nd ] [ DRG ] repeatedly until the
unit you want is displayed.
¾
90 deg. = 1.57079632679 rad. = 100 grad.
DEG
[ 2nd ] [ DRG ]
0
.
RAD
9 0
O
=
90 [ 2nd ] [ DRG ]
1 .
5 7 0 7 9 6 3 2 6 7 9
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-E15-
GRAD
1
.
5 7 0 7 9 6 3 2 6 7
[ 2nd ] [ DRG ]
1 0 0
.
Sexagesimal
↔
Decimal transformation
The calculator enables you to convert the sexagesimal figure (degree,
minute and second) to decimal notation by pressing [
] or
convert the decimal notation to the sexagesimal notation by [ 2nd ]
[
].
Sexagesimal figure value display is as follow :
125
45
׀
30
׀
׀
55
Represent 125 degrees (D),
45 minutes(M), 30.55 seconds(S)
(Note) : The total digits of D, M and S and separator marks must be
within 12 digits, or the sexagesimal couldn't be shown
completely.
¾
12.755 = 12
45
l
18
l l
DEG
12.755 [ 2nd ] [
]
1 2
4 5
l
1 8
l l
¾
2
45
l
10.5
l l
= 2.75291666667
DEG
2 [
] 45 [
] 10.5 [
]
2
.
7 5 2 9 1 6 6 6 6 6 7
Trigonometric / Inverse-Tri. functions
SR-281N
provides standard trigonometric functions and inverse
trigonometric functions - sin, cos, tan, sin
–1
, cos
–1
and tan
–1
.
(Note) : When using those keys, make sure the calculator is set for the
angle unit you want.
¾
sin 30 deg.= 0.5
DEG
s i n 3 0 =
[ sin ] 30 [=]
0
.
5
¾
3 cos (
π
3
2
rad) = – 1.5
RAD
3
¼
c o s ( 2
¼
π
3 =
3 [ cos ] [ ( ] 2 [ x ] [ 2nd ] [
π
] [ ]
3 [=]
– 1
.
5
File name : CBM_SR-281N_IB_English_black_v09330.doc
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-E16-
¾
3 sin
–1
0.5 = 90 deg
DEG
3
¼
s i n
–1
0
.
5 =
3 [ 2nd ] [ sin
–1
] 0.5 [=]
9 0
.
Hyperbolic / Inverse-Hyp. functions
SR-281N
uses [ 2nd ] [ HYP ] to calculate the hyperbolic functions and
inverse-hyperbolic functions - sinh, cosh, tanh, sinh
–1
, cosh
–1
and
tanh
–1
.
(Note) : When using those keys, make sure the calculator is set for the
angle unit you want.
¾
cosh 1.5 + 2 = 4.35240961524
DEG
c o s h 1
.
5 + 2 =
[ 2nd ] [ HYP ] [ cos ] 1.5 [ + ] 2 [=]
4
.
3 5 2 4 0 9 6 1 5 2 4
¾
sinh
–1
7 = 2.64412076106
DEG
s i n h 1
–1
7 =
[ 2nd ] [ HYP ] [ 2nd ] [ sin
–1
] 7 [=]
2
.
6 4 4 1 2 0 7 6 1 0 6
Coordinates transformation
Rectangular Coordinates
Polar Coordinates
x + y i = r (cos
θ
+ i sin
θ
)
(Note) : When using those key, make sure the calculator is set for the
angle unit you want.
The calculator can perform the conversion between rectangular
coordinates and polar coordinates by [ 2nd ] [ P R ] and [ 2nd ]
[ R P ].
¾
If x = 5, y = 30, what are r,
θ
? Ans : r = 30.4138126515,
θ
= 80.537677792
o
DEG
( )
R
P ( 5
,
[ 2nd ]
[ R P ] 5 [ 2nd ] [ ] 30
3 0
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-E17-
DEG
r
[=]
3 0
.
4 1 3 8 1 2 6 5 1 5
DEG
θ
[ 2nd ] [ X
↔
Y ]
8 0
.
5 3 7 6 7 7 7 9 2
¾
If r = 25,
θ
= 56
o
what are x, y ? Ans : x = 13.9798225868,
y = 20.7259393139
DEG
( )
P
R ( 2 5
,
[ 2nd ] [ P R ] 25 [ 2nd ] [ ] 56
5 6
DEG
X
[=]
1 3
.
9 7 9 8 2 2 5 8 6 8
DEG
Y
[ 2nd ] [ X
↔
Y ]
2 0
.
7 2 5 9 3 9 3 1 3 9
Probability
This calculator provides the following probability functions :
[ nPr ] Calculates the number of possible permutations of n item
taken r at a time.
[ nCr ] Calculates the number of possible combinations of n items
taken r at a time.
[ x ! ]
Calculates the factorial of a specified positive integer n,
where n
≦
69.
[ RND ] Generates a random number between 0.000 and 0.999
¾
840
!
]
)
4
7
(
[
!
7
=
−
DEG
7 P 4 =
7 [ 2nd ] [ nPr ] 4 [=]
8 4 0
.
¾
5
3
!
]
)
4
7
(
[
!
4
!
7
=
−
DEG
7 C 4 =
7 [ 2nd ] [ nCr ] 4 [=]
3 5
.
File name : CBM_SR-281N_IB_English_black_v09330.doc
Date: 2009/3/30 Trimmed Size : 140 x 75 mm SCALE 1 : 1
-E18-
¾
5 ! = 120
DEG
5 ! =
5 [ 2nd ] [ x ! ] [=]
1 2 0
.
¾
Generates a random between 0.000 ~ 0.999
DEG
R n d
[ 2nd ] [ RND ]
0
.
4 4 9
Other functions ( 1/x,
,
3
,
X
, x
2
, x
3
, x
y
, INT,
FRAC )
The calculator also provides reciprocal ( [ 2nd ] [ 1/x ] ), square root
( [
√
] ), cubic root ( [ 2nd ] [
3
] ), universal root ( [ 2nd ] [
X
] ),
square ( [ x
2
] ), cubic ( [ 2nd ] [ x
3
] ), and exponentiation ( [ x
y
] )
functions.
¾
8
.
0
.25
1
1
=
DEG
1
.
2 5
–1
=
1.25 [ 2nd ] [ 1 / x ] [=]
0
.
8
¾
139
=
5
+
125
+
21
+
4
+
2
3
3
2
DEG
2
2
+
√
( 4 + 2 1 ) +
2 [ x
2
] [ + ] [
√
] [ ( ] 4 [ + ] 21 [ ) ]
[ + ] [ 2nd ] [
3
] 125 [ + ] 5 [ 2nd ]
[ x
3
] [=]
1 3
9
.
¾
16812
=
625
+
7
4
5
DEG
7 x
y
5 + 4
X
√
6 2 5 =
7 [ x
y
] 5 [ + ] 4 [ 2nd ] [
X
] 625 [=]
1 6 8 1
2
.
INT
Indicate the integer part of a given number
FRAC Indicate the fractional part of a given number
¾
INT ( 10 8 ) = INT ( 1.25 ) = 1
DEG
I N T ( 1 0
8 =
[ 2nd ] [ INT ] 10 [ ] 8 [=]
1
.
¾
FRAC ( 10 8 ) = FRAC ( 1.25 ) = 0.25
DEG
F R A C ( 1 0
8 =
[ 2nd ] [ FRAC ] 10 [ ] 8 [=]
0
.
2 5
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-E19-
Unit Conversion
The calculator has a built-in unit conversion feature that enables you to
convert numbers among different units.
1. Enter the number you want to convert.
2. Press [ CONV ] to display the menu. There are 7 menus, covering
distance, area, temperature, capacity, weight, energy, and
pressure.
3. Use the [ CONV ] to scroll through the list of units until a
appropriate units menu is shown, then [=].
4. Pressing
[ ] or [ 2nd ] [
] can convert the number to
another unit.
¾
1 y d
2
= 9 f t
2
= 0.00000083612 km
2
DEG
f t
2
y d
2
m
2
1 [ CONV ] [ CONV ] [
] [=]
1
.
DEG
f t
2
y d
2
m
2
[ 2nd ] [
]
9
.
DEG
k m
2
h e c t a r e s
[
] [
] [
]
0
.
0 0 0 0 0 0 8 3 6 1 2
Physics constants
You can use 136 physics constants in your calculations. With the
following constants :
Data is referred to Peter J.Mohr and Barry N.Taylor, CODATA
Recommended Values of the Fundamental Physical Constants:1998,
Journal of Physical and Chemical Reference Data,Vol.28, No.6,1999
and Reviews of Modern Physics,Vol.72, No.2, 2000.
No. Quantity Symbol
Value,
Unit
1.
Speed of light in vacuum
c
299792458 m s
–1
2. Magnetic
constant
μ
0
1.2566370614 x10
–6
N A
–2
3. Electric
constant
ε
0
8.854187817 x 10
–12
F m
–1
4.
Characteristic impedance
of vacuum
Z
0
376.730313461
Ω
5.
Newtonian constant of
gravitation
G 6.67310
x10
–11
m
3
kg
–1
s
–2
6. Planck
constant
h
6.6260687652 x10
–34
J s
7.
Planck constant over 2 pi
h
1.05457159682 x10
–34
J s
8. Avogadro
constant
N
A
6.0221419947 x10
23
mol
–1
9. Planck
length
lp
1.616012 x10
–35
m
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-E20-
10. Planck
time
tp
5.390640 x10
–44
s
11. Planck
mass
mp
2.176716 x10
–8
kg
12. Atomic mass constant
m
μ
1.6605387313 x10
–27
kg
13. Atomic mass constant
energy equivalent
m
μ
c
2
1.4924177812 x10
–10
J
14. Faraday
constant
IF
96485.341539 C mol
–1
15. Elementary
charge
e
1.60217646263
x10
–19
C
16. Electron volt–joule
relationship
eV 1.60217646263
x10
–19
J
17. Elementary charge over h
e/h
2.41798949195 x10
14
AJ
–1
18. Molar gas constant
R
8.31447215 J mol
–1
K
–1
19. Boltzmann
constant
k
1.380650324 x10
–23
J K
–1
20. Molar planck constant
N
A
h 3.99031268930x10
–10
Js mol
–1
21. Sackur–Tetrode
constant
S
0
/R
–
1.164867844
22. Wien displacement law
constant
b 2.897768651
x10
–3
m K
23. Lattice parameter of
silicon
a 543.10208816
x10
–12
m
24.
Stefan–Boltzmann constant
σ
5.67040040 x10
–8
W m
–2
K
–4
25. Standard acceleration of
gravity
g
9.80665 m s
–2
26. Atomic mass
unit–kilogram relationship
μ
1.6605387313 x10
–27
kg
27. First radiation constant
c
1
3.7417710729 x10
–16
Wm
2
28. First radiation constant for
spectral radiance
c
1
L
1.19104272293x10
–16
Wm
2
sr
–1
29. Second radiation constant
c
2
1.438775225 x10
–2
m K
30. Molar volume of ideal gas
Vm
22.41399639 x10
–3
m
3
mol
–1
31. Rydberg
constant
R
∞
10973731.5685 m
–1
32. Rydberg constant in Hz
R
∞
c
3.28984196037 x10
15
Hz
33.
Rydberg constant in joules
R
∞
hc
2.1798719017 x10
–18
J
34. Hartree
energy
E
h
4.3597438134 x10
–18
J
35. Quantum of circulation
h/me
7.27389503253 x10
–4
m
2
s
–1
36. Fine structure constant
α
7.29735253327 x10
–3
37. Loschmidt
constant
n
0
2.686777547
x10
25
m
–3
38. Bohr
radius
a
0
0.52917720832
x10
–10
m
39. Magnetic flux quantum
Φ
0
2.06783363681 x10
–15
Wb
40. Conductance
quantum
G
0
7.74809169628
x10
–5
S
41. Inverse of conductance
quantum
G
0
–1
12906.4037865
Ω
42. Josephson
constant
KJ
483597.89819 x10
9
Hz V
–1
43. Von Klitzing constant
RK
25812.8075730
Ω
44. Bohr
magneton
μ
B
927.40089937 x10
–26
J T
–1
45. Bohr magneton in Hz/T
μ
B/h
13.9962462456 x10
9
Hz T
–1
46. Bohr magneton in K/T
μ
B/k
0.671713112 K T
–1
47. Nuclear
magneton
μ
N
5.0507831720 x10
–27
J T
–1
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-E21-
48.
Nuclear magneton in MHz/T
μ
N/h
7.6225939631 MHz T
–1
49. Nuclear magneton in K/T
μ
N/k
3.658263864 x10
–4
K T
–1
50. Classical electron radius
re
2.81794028531 x10
–15
m
51. Electron
mass
me
9.1093818872 x10
–31
kg
52. Electron mass energy
equivalent
mec
2
8.1871041464 x10
–14
J
53.
Electron–muon mass ratio
me/m
μ
4.8363321015 x10
–3
54. Electron–tau mass ratio
me/m
τ
2.8755547 x10
–4
55. Electron–proton mass
ratio
me/mp
5.44617023212 x10
–4
56. Electron–neutron mass
ratio
me/mn
5.43867346212 x10
–4
57. Electron–deuteron mass
ratio
me/md
2.72443711706x10
–4
58. Electron charge to mass
quotient
–
e/me
–
1.75882017471 x10
11
Ckg
–1
59. Compton
wavelength
λ
c
2.42631021518 x10
–12
m
60. Compton wavelength over
2 pi
λ
c
386.159264228 x10
–15
m
61. Thomson cross section
σ
e
0.66524585415 x10
–28
m
2
62. Electron magnetic
moment
μ
e
–
928.47636237x10
–26
J T
–1
63.
Electron magnetic
moment to Bohr
magneton ratio
μ
e/
μ
B
–
1.00115965219
64.
Electron magnetic
moment to nuclear
magneton ratio
μ
e/
μ
N
–
1838.28196604
65. Electron–muon magnetic
moment ratio
μ
e/
μ
μ
206.766972063
66. Electron–proton magnetic
moment ratio
μ
e/
μ
p
–
658.210687566
67. Electron–neutron
magnetic moment ratio
μ
e/
μ
n
960.9205023
68. Electron–deuteron
magnetic moment ratio
μ
e/
μ
d
–
2143.92349823
69.
Electron to shielded helion
magnetic moment ratio
μ
e/
μ
'h
864.05825510
70. Electron magnetic
moment anomaly
a e
1.15965218694 x10
–3
71. Electron
g–factor
g e
–
2.00231930437
72.
Electron gyromagnetic ratio
γ
e
1.76085979471 x10
11
s
–1
T
–1
73. Muon
mass
m
μ
1.8835310916 x10
–28
kg
74. Muon mass energy
equivalent
m
μ
c
2
1.6928333214 x10
–11
J
75. Muon–tau mass ratio
m
μ
/m
τ
5.9457297 x10
–2
76. Muon–proton mass ratio
m
μ
/mp
0.11260951733
77. Muon–neutron mass ratio
m
μ
/mn
0.11245450793
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-E22-
78. Muon magnetic moment
anomaly
a
μ
1.1659160264 x10
–3
79. Muon
g–factor
g
μ
–
2.00233183201
80. Muon Compton
wavelength
λ
c,
μ
11.7344419735 x10
–15
m
81. Muon Compton
wavelength over 2 pi
λ
c,
μ
1.86759444455 x10
–15
m
82. Muon magnetic moment
μ
μ
–
4.4904481322x10
–26
J T
–1
83. Muon magnetic moment
to Bohr magneton ratio
μ
μ
/
μ
B
–
4.8419708515 x10
–3
84. Muon magnetic moment to
nuclear magneton ratio
μ
μ
/
μ
N
–
8.8905977027
85. Muon–proton magnetic
moment ratio
μ
μ
/
μ
p
–
3.1833453910
86. Tau Compton wavelength
λ
c,
τ
0.6977011 x10
–15
m
87. Tau Compton wavelength
over 2 pi
λ
c,
τ
0.11104218 x10
–15
m
88. Tau
mass
m
τ
3.1678852 x10
–27
kg
89. Tau mass energy
equivalent
m
τ
c
2
2.8471546 x10
–10
J
90. Tau–proton mass ratio
m
τ
/mp
1.8939631
91. Proton Compton
wavelength
λ
c,p
1.32140984710 x10
–15
m
92. Proton Compton
wavelength over 2 pi
λ
c,p
0.21030890892 x10
–15
m
93. Proton
mass
mp
1.6726215813 x10
–27
kg
94. Proton mass energy
equivalent
mpc
2
1.5032773112 x10
–10
J
95. Proton–neutron mass
ratio
mp/mn
0.99862347856
96. Proton charge to mass
quotient
e/mp
9.5788340838 x10
7
C kg
–1
97. Proton magnetic moment
μ
p
1.41060663358 x10
–26
J T
–1
98. Shielded proton magnetic
moment
μ
'p
1.41057039959 x10
–26
J T
–1
99. Proton magnetic moment
to nuclear magneton ratio
μ
p/
μ
N
2.79284733729
100. Proton–neutron magnetic
moment ratio
μ
p/
μ
n
–
1.4598980534
101.
Shielded proton magnetic
moment to Bohr
magneton ratio
μ
'p/
μ
B
1.52099313216 x10
–3
102. Proton gyromagnetic ratio
γ
p
2.6752221211 x10
8
s
–1
T
–1
103. Shielded proton
gyromagnetic ratio
γ
'p
2.6751534111 x10
8
s
–1
T
–1
104. Proton magnetic shielding
correction
σ
'p
25.68715 x10
–6
105. Proton g–factor
g p
5.58569467557
106. Neutron Compton
wavelength
λ
c,n
1.31959089810 x10
–15
m
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-E23-
107. Neutron Compton
wavelength over 2 pi
λ
c,n
0.21001941422 x10
–15
m
108. Neutron mass
mn
1.6749271613 x10
–27
kg
109. Neutron mass energy
equivalent
mnc
2
1.5053494612 x10
–10
J
110. Neutron magnetic
moment
μ
n
–
0.9662364023x10
–26
J T
–1
111.
Neutron magnetic
moment to Bohr
magneton ratio
μ
n/
μ
B
–1.0418756325 x10
–3
112. Neutron g–factor
gn
–
3.8260854590
113. Neutron gyromagnetic
ratio
γ
n
1.8324718844 x10
8
s
–1
T
–1
114. Deuteron mass
md
3.3435830926 x10
–27
kg
115. Deuteron mass energy
equivalent
mdc
2
3.0050626224 x10
–10
J
116. Deuteron molar mass
M(d)
2.01355321271x10
–3
kg
mol
–1
117. Deuteron–electron mass
ratio
md/me
3670.48295508
118. Deuteron–proton mass
ratio
md/mp
1.99900750083
119. Deuteron magnetic
moment
μ
d
0.43307345718 x10
–26
J T
–1
120.
Deuteron magnetic
moment to Bohr
magneton ratio
μ
d/
μ
B
0.46697545565 x10
–3
121.
Deuteron magnetic
moment to nuclear
magneton ratio
μ
d/
μ
N
0.85743822849
122. Deuteron–proton
magnetic moment ratio
μ
d/
μ
p
0.30701220835
123. Helion mass
mh
5.0064117439 x10
–27
kg
124. Helion mass energy
equivalent
mhc
2
4.4995384835 x10
–10
J
125. Helion molar mass
M(h)
3.01493223470x10
–3
kg mol
–1
126. Helion–electron mass
ratio
mh/me
5495.88523812
127. Helion–proton mass ratio
mh/mp
2.99315265851
128. Shielded helion magnetic
moment
μ
'h
–
1.07455296745 x10
–26
J T
–1
129.
Shielded helion magnetic
moment to Bohr
magneton ratio
μ
'h/
μ
B
–
1.15867147414 x10
–3
130.
Shielded helion magnetic
moment to nuclear
magneton ratio
μ
'h/
μ
N
–
2.12749771825
131. Shielded helion
gyromagnetic ratio
γ
'h
2.03789476485 x10
8
s
–1
T
–1
132. Alpha particle mass
m
α
6.6446559852 x10
–27
kg
133. Alpha particle mass
energy equivalent
m
α
c
2
5.9719189747 x10
–10
J
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134. Alpha particle molar mass
M(
α
)
4.00150617471 x10
–3
kg
mol
–1
135. Alpha particle to electron
mass ratio
m
α
/me
7294.29950816
136. Alpha particle to proton
mass ratio
m
α
/mp
3.97259968461
To insert a constant at the cursor position :
1. Press [ CONST ] to display the physics constants menu.
2. Press
[ ] or [ 2nd ] [
] until the constant you want is
underlined.
3. Press
[=].
You also can use the [ CONST ] key in combination with a number, 1
through 136, to recall a physical constants. For example, press 15
[ CONST ].
DEG
e
1
.
6 0 2 1 7 6 4 6 2 6 3
–19
¾
3 x N
A
= 1.80664259841 x 10
24
CONST
DEG
h
h
N
A
l p
t p
3 [ x ] [ CONST ] [ CONST ] [
]
[
]
6
.
0 2 2 1 4 1 9 9 4 7
23
CONST
DEG
0 0 8
:
m o l
–1
[=]
6
.
0 2 2 1 4 1 9 9 4 7
23
CONST
DEG
3
¼
N
A
=
[=] [=]
1
.
8 0 6 6 4 2 5 9 8 4 1
24
Base–n
calculations
Use MAIN ( [ MODE ] 1 ( MAIN ) ) mode for Base–n calculations.
The unit enables you to calculate in number base other than decimal.
The calculator can add, subtract, multiply, and divide binary, octal, and
hexadecimal numbers.
The following shows the numerals that can be used in each number
base.
Binary base ( b ) : 0, 1
Octal base ( o ) : 0, 1, 2, 3, 4, 5, 6, 7
Decimal base : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Hexadecimal base ( h ) : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
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To distinguish the A, B, C, D, E and F used in the hexadecimal base
from standard letters, they appear as shown in the below.
Key
Display
(Upper)
Display
(Lower)
Key
Display
(Upper)
Display
(Lower)
A /A
D
ID
B IB
E
IE
C
I
C
F
IF
Select the number base you want to use with [ BIN ], [ OCT ],
[ DEC ], [ HEX ]. The " BIN ", " b ", " OCT ", " o ", " HEX ", " h "
indicators show you which number base you are using. If none of the
indictors appears in the display, you are in decimal base.
Bases conversions
¾
37 (base 8) = 31 (base 10) = 1F (base 16)
DEG
OCT
[ 2nd ] [ OCT ] 37
0 0 0 0 0 0 0 0 0 3 7
o
DEG
[ 2nd ] [ DEC ]
3 1
.
DEG
HEX
[ 2nd ] [ HEX ]
0 0 0 0 0 0 1 F
h
Block Function
For a result in binary base, it will be displayed using block function.
The maximum of 32 digits are displayed in 4 blocks of 8 digits.
1 1 0 1 0 0 1 1 b
DEG BIN
Indicates total blocks : 1 block
Indicates Block 1 presently displayed
Indicates Block 2 presently displayed
Indicates Block 3 presently displayed
Indicates Block 4 presently displayed
Indicates total blocks : 2 blocks
Indicates total blocks : 3 blocks
Indicates total blocks : 4 blocks
The block function comprises upper and lower block indicators. The
upper indicator means current block position, and the lower indicator
means total blocks for a result.
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In the binary base, the block 1 is displayed immediately after
calculation. Other blocks ( block 2 ~ block 4 ) are displayed by pressing
[
].
For example, input 47577557
16
Press [ 2nd ] [ HEX ] 47577557
[ 2nd ] [ BIN ]
0 1 0 1 0 1 1 1
b
DEG BIN
– –
Indicates Block 1 presently displayed
[
]
0 1 1 1 0 1 0 1
b
DEG BIN
–
–
Indicates Block 2 presently displayed
[
]
0 1 0 1 0 1 1 1
b
DEG BIN
– –
Indicates Block 3 presently displayed
[
]
0 1 0 0 0 1 1 1
b
DEG BIN
– – –
Indicates Block 4 presently displayed
47577557
16
= Block 4 + Block 3 + Block 2 + Block 1
= 01000111010101110111010101010111
2
Basic arithmetic operations for bases
¾
1IEIF
16
+ 1234
10
1001
2
= 1170
8
DEG
OCT
h 1 IE IF + 1 2 3 4
b 1
[ 2nd ] [ HEX ] 1E F [ + ] [ 2nd ]
[ DEC ] 1234 [ ] [ 2nd ] [ BIN ]
1001 [=] [ 2nd ] [ OCT ]
0 0 0 0 0 0 0 1 1 7 0
o
Negative expressions
In binary, octal, and hexadecimal bases, the calculator represents
negative numbers using complement notation.
The complement is the result of subtracting that number from
100000000000000000000000000000000 in that number's base by
pressing [ NEG ] key in non-decimal bases.
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¾
3/A
16
= NEG IFIFIFIFIFIFIC6
16
DEG
HEX
N E G
h 3 /A
[ 2nd ] [ HEX ] 3 A [ NEG ]
F F F F F F C 6
h
Logical operation
Logical operations are performed through logical products (AND),
negative logical (NAND), logical sums (OR), exclusive logical sums
(XOR), negation (NOT), and negation of exclusive logical sums
(XNOR).
¾
1010
2
AND ( /A
16
OR 7
16
) = 12
8
DEG
OCT
b 1 0 1 0
A N D
( h
[ 2nd ] [ BIN ] 1010 [ AND ] [ ( ] [ 2nd ]
[ HEX ] A [ OR ] 7 [ ) ] [=]
[ 2nd ] [ OCT ]
0 0 0 0 0 0 0 0 0 1 2
o
Statistical
Calculations
Use STAT ( [ MODE ] 2 ( STAT ) ) mode for statistical calculations.
The calculators can perform both single–variable statistical
calculations and paired–variable in this mode.
Press [ MODE ] 2 ( STAT ) to enter STAT mode. There are six items in
STAT mode, asking you to select one of them,
DEG
1–VAR LIN LOG
STAT
[
] [
] [
]
DEG
EXP PWR D–CL
STAT
Single–variable statistics
1–VAR Single–variable statistics
Paired-variable / Regression statistics
LIN
Linear Regression
y = a + b x
LOG
Logarithmic Regression
y = a + b lnx
EXP
Exponential Regression
y = a • e
bx
POW
Power Regression
y = a • x
b
D–CL
Clear all statistical data
Entering data
Always make sure you clear statistical data by D–CL before performing
statistical calculations.
(A) To input single–variable data using the following syntaxes :
# Individual data : [ DATA ] < x value >
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# Multiple data of the same value :
[ DATA ] < x value > [ x ] < Number of repeats >
(B) To input paired–variable / regression data using the following
syntaxes :
# Individual data-set : [ DATA ] < x value > [ ] < y value >
# Multiple data of the same value :
[ DATA ] < x value > [ ] < y value > [ x ] < Number of repeats >
(Note) : Even you exit STAT mode, all data are still retained unless you
clear all data by selecting D-CL mode.
Displaying results
The values of the statistical variables depend on the data you input.
You can recall them by the key operations shown in the below table.
Single–variable statistics calculations
Variables Meaning
n ( [ n ] )
Number of the x values entered
x
( [2nd]+[
x
] )
Mean of the x values
Sx
( [2nd]+[
Sx
] )
Sample standard deviation of x values
σ
x
( [2nd]+[
σ
x
] )
Population standard deviation of x values
∑
x
( [2nd]+[
∑
x
] ) Sum of all x values
∑
x
2
( [2nd]+[
∑
x
2
]) Sum of all x
2
values
CP
( [2nd]+[
CP
] ) Potential capability precision of the x values
CPK ( [CPK] )
Minimum (CPU, CPL) of the x values, where
CPU is upper spec. limit of capability
precision and CPL is lower spec. limit of
capability precision
CPK = Min ( CPU , CPL ) = CP ( 1 – Ca )
Paired-variable statistics / Regression calculations
Variables Meaning
n ( [ n ] )
Number of x-y pairs entered
x
( [2nd]+[
x
] )
y
( [2nd]+[
y
] )
Mean of the x values or y values
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Sx
( [2nd]+[ Sx ] )
Sy
( [2nd]+[ Sy ] )
Sample standard deviation of x values or y
values
σ
x
( [2nd]+[
σ
x
] )
σ
y
( [2nd]+[
σ
y
] )
Population standard deviation of x values or
y values
∑
x
( [2nd]+[
∑
x
] )
∑
y
( [2nd]+[
∑
y
] )
Sum of all x values or y values
∑
x
2
( [2nd]+[
∑
x
2
])
∑
y
2
( [2nd]+[
∑
y
2
])
Sum of all x
2
values or y
2
values
∑
x y
Sum of ( x • y ) for all x-y pairs
CP
( [2nd]+[
CP
] ) Potential capability precision of the x values
CPK ( [ CPK ] )
Minimum (CPU, CPL) of the x values, where
CPU is upper spec. limit of capability
precision and CPL is lower spec. limit of
capability precision
CPK = Min ( CPU , CPL ) = CP ( 1 – Ca )
a ( [2nd]+[
a ] )
Regression formula constant term a
b ( [2nd]+[
b ] )
Regression formula regression coefficient b
r ( [2nd]+[
r ] )
Correlation coefficient r
x
’
([ x
’
] )
Estimated value of x
y
’
([ y
’
] )
Estimated value of y
You also can add a new data anytime. The unit automatically
recalculates statistics each time you press [ DATA ] and enter a new
data value.
¾
Enter data : USL
= 95, LSL = 70, DATA 1 = 75, DATA 2 = 85, DATA
3 = 90, DATA 4 = 82, DATA 5 = 77, then find out n = 5, = 81.8,
Sx = 6.05805249234,
σ
x = 5.41848687366, CP = 0.76897236513,
and CPK = 0.72590991268
DEG
STAT
1–
V A R
L I N
L O G
[ MODE ] 2
DEG
STAT
D A T A
5
[=] [ DATA ] 75 [ DATA ] 85 [ DATA ] 90
[ DATA ] 82 [ DATA ] 77
7 7
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DEG
STAT
n
[ n ]
5
.
DEG
STAT
x
[ 2nd ] [
x
]
8 1
.
8
DEG
STAT
S x
[ 2nd ] [ Sx ]
6
.
0 5 8 0 5 2 4 9 2 3 4
DEG
STAT
σ
x
[ 2nd ] [
σ
x ]
5
.
4 1 8 4 8 6 8 7 3 6 6
DEG
STAT
U S L =
[ 2nd ] [ CP ] 95
9 5
CP
USL
DEG
STAT
L S L =
[=] 70
7 0
CP
LSL
DEG
STAT
C P
[=]
0
.
7 6 8 9 7 2 3 6 5 1 3
DEG
STAT
U S L =
[ CPK ]
9 5
.
CPK
USL
DEG
STAT
L S L =
[=]
7 0
.
CPK
LSL
DEG
STAT
C P K
[=]
0
.
7 2 5 9 0 9 9 1 2 6 8
¾
Find a, b and r for the following data using linear regression and
estimate x = ? for y =573 and y = ? for x = 19.
Data
item
15 17 21 28
FREQ. 451 475 525 678
DEG
STAT
1–
V A R
L I N
L O G
[ MODE ] 2 [
]
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DEG
STAT
D A T A
4 = 2 8
,
[=] [ DATA ] 15 [ ] 451 [ DATA ] 17
[ ] 475 [ DATA ] 21 [ ] 525 [ DATA ]
28 [ ] 678
6 7 8
REG
DEG
STAT
a
[ 2nd ] [ a ]
1 7 6
.
1 0 6 3 2 9 1 1 4
REG
DEG
STAT
b
[ 2nd ] [ b ]
1 7
.
5 8 7 3 4 1 7 7 2 2
REG
DEG
STAT
r
[ 2nd ] [ r ]
0
.
9 8 9 8 4 5 1 6 4 1 3
REG
DEG
STAT
x
’
5 7 3
573 [ x
’
]
2 2
.
5 6 7 0 0 7 3 4 1 3
REG
DEG
STAT
y
’
1 9
19 [ y
’
]
5 1 0
.
2 6 5 8 2 2 7 8 5
REG
Deleting data
The method to delete data depends on whether you have already
stored the data by next pressing [ DATA ] key or not.
To delete data you just input but have not yet stored it by next pressing
[ DATA ] , simple press [ CE ].
To delete data that you have already stored by next pressing [ DATA ] ,
(A) To delete single–variable data using the following syntaxes :
# < x value > [ 2nd ] [ DEL ]
# < x value > [ x ] < Number of repeats > [ 2nd ] [ DEL ]
(B) To delete paired–variable / regression data using the following
syntaxes:
# Individual data-set : < x value > [ ] < y value > [ 2nd ] [ DEL ]
# Multiple data-set with the same value :
< x value > [ ] < y value > [ x ] < Number of repeats > [ 2nd ]
[ DEL ]
If you enter and delete a value that isn't included in the stored data by
mistake, " dEL Error " appears, but the previous data are still retained.
Editing data
Press [ 2nd ] [ EDIT ] to enter EDIT mode. The EDIT mode is
convenient and friendly for you to view, correct, delete data.
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(A) In 1–VAR mode, the method to view data depends on whether you
want to view data item or not.
# Each time you press [ DATA ], first data item appears 1 second
and then the corresponding value.
[ DATA ]
DEG
dAtA 1
STAT
EDIT
1 second
DEG
15.
STAT
EDIT
# Each time you press [=], value appears directly on the display
without data item.
[=]
DEG
15.
STAT
EDIT
(B) In
REG mode, each time you press [ DATA ], data item and x value
appear on the screen at the same time. You can press [ ] to
switch between x and y value.
[ DATA ]
DEG
DATA 1 = 15 , 45
STAT
15
EDIT
[ ]
DEG
DATA 1 = 15 , 45
STAT
451
EDIT
If you want to correct data, find out and enter a new entry to replace it.
FULL message
A “ FULL” is indicated when any of the following conditions occur and
further data entry becomes impossible. Just pressing any key can
clear the indicator. The previous data entries are still retained unless
you exit STAT mode.
1) If the times of data entry by [ DATA ] is more than 50
2) The number of repeats is more than 255
3) n
>
12750 (n = 12750 appears when the times of data entry by
[ DATA ] are up to 50 and the number of repeats for each value
are all 255, i.e. 12750 = 50 x 255 )
Complex
Calculations
Use CPLX ( [ MODE ] 3 ( CPLX ) ) mode for complex calculations.
Complex mode enables you to add, subtract, multiply, and divide
complex numbers.
The results of a complex operation are displayed as follow :
Re
Real value
Im
Imaginary value
ab
Absolute value
ar
Argument value
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¾
( 7 – 9 i ) + ( 15 + 12 i ) = 22 + 3 i , ab = 22.2036033112, ar =
7.76516601843
CPLX
DEG
[ MODE ] 3
0
.
CPLX
DEG
R e
I m
a b
a r
7 [ – ] 9 [ i ] [ + ] 15 [ + ] 12 [ i ] [=]
2 2
.
CPLX
DEG
R e
I m
a b
a r
[
]
3
.
i
CPLX
DEG
R e
I m
a b
a r
[
]
2 2
.
2 0 3 6 0 3 3 1 1 2
CPLX
DEG
R e
I m
a b
a r
[
]
7
.
7 6 5 1 6 6 0 1 8 4 3
