Calculating Estimated Values; Performing Normal Distribution Calculations - Casio fx-115ES PLUS User Manual

.
.£,.£" .£, and yare not variables. They are commands of the type that take
an argument immediately before them. See "Calculating Estimated Values.
for more information.
Minimum Value: minX., minY, Maximum Value: maxX., maxY
@!!)II) (STAT/DIST) lID(MinMax) II) to rn
(When the single-variable statistical calculation is selected.)
@!!)II) (STAT/DIST) lID (MinMax) II) to (!)
(When a paired-variable statistical calculation is selected.)
First Quartile: Qt, Median: med, Third Quartile: Q3
I!!iIII)(STAT/DIST) lID(MinMax) lID to (ID
(When the single-variable statistical calculation is selected.)
Note: While single-variable statistical calculation is selected, you can input
the functions and commands for performing normal distribution calculation
from the menu that appears when you perform the following key operation:
@!!)II) (STAT/DIST) (ID(Distr). See "Performing Normal Distribution
Calculations. for details.
h
To input the single-variable data x = (t, 2, 2, 3, 3, 3, 4, 4, 5), using
the FREQ column to specify the number of repeats for each items
(Ix.; freq.)
=
{1;1, 2;2, 3;3, 4;2, 5;1)), and calculate the mean and
population standard deviation.
@!!)1i!ID(SETUP)<i>(!)(STAT)II)(ON)
@J1ID(STAT)II)(1-VAR)
1§)2§)3§)4§)5§)<i><E>
113213313213
_
1!9@!!) II)(STAT/DIST)(!){Var)rn{x)§)
[
1!9@!!) II) {STAT/DIST)(!){Var)lID (crx)13
[
STAt
iii
~I' ~I~I
~
L
1547005381
Results: Mean: 3 Population Standard Deviation: 1.154700538
~
To calculate the linear regression and logarithmic regression
correlation coefficients 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 decimalplaces) for resulls.
@!!)~(SETUP)<i> (!){STAT) rn (OFF)
@!jJ1i!ID(SETUP)IID(Fix)1ID
@)1ID(STAT)rn(A+BX)
20 13 110 13 200 13 290 13 <i> <E\
315013 7310 138800 13 931013
.
@@!jJII)(STATIDIST)(ID(Reg)lID(r)§)
[
1!91!!i11I)(STAT/DIST)II)(Type)(!)(ln X)
1!91!!i11I)(STAT/DIST)(ID(Reg)lID(r)§)
[
@1!!iI1I)(STAT/DIST)IID(Reg)II)(A)§)
[
E-31
SfAT IiJ FIX
'
I
Keaa
l
~BDa
l
~ ... .iiII
0.9231
0.9981
-3857.9841
@Iffi II)(STATIDIST) (ID(Reg) r n (B)13
1 2357.5321
Results: Linear Regression Correlation Coefficient: 0.923
logarithmic Regression Correlation Coefficient: 0.998
logarithmic Regression Formula: y
=
-3857.984 + 2357.5321nx
j
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. and x" 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
h.
Specify Fix 3 for the result. (Perform the following operation
after completing the operations in
h.)
@ 1601mII){STATIDIST) (ID(Reg) (IDlY) 13
1 8106.8981
Result: 8106.898
Important: Regression coefficient, correlation coefficient, and estimated
value calculations can take considerable time when there are a large number
of data items.
Performing Normal Distribution Calculations
While single-variable statistical calculation is selected, you can perform
normal distribution calculation using the functions shown below from
the menu that appears when you perform the following key operation:
@!!)
II) (STA T/DIST)
( ID{Distr).
P, Q, R: These functions take the argument t and determine a probability of
standard normal distribution as illustrated below.
AJeAX
o tOt 0 t
~t:
This function is preceded by the argument X, and determines the
normalized variate X.t _X~i .
h
For the singlevariabledata {x. ; fraq.}= (0;1, 1;2,2;1,3;2,4;2,5;2,
6;3,7;4,9;2, 10;1), to determine the normalized variate (~r) when x
= 3, and P(t) at that point up to three decimal places (Fix 3).
@!!)@)(SETUP)<i>(!)(STAT)II){ON)
@!!)@ii!)(SETUP)IID(Fix)IID@J lID(STAT)
1 I)(1-V AR)
013 113213313413513613713913 s;." F~~U f IX
10§)$<E\1 132131 13213213213313
Iyl lal~1
413213113
E-32