CNATRAINST 1500.4F

18 May 1999

ALTERNATE METHOD FOR COMPUTING STANDARD DEVIATION

The general formula for the standard deviation is:

where

d

= each score's difference from mean score

N

= number of scores

S.D. = Standard Deviation

An alternate method useful for automated databases or for hand

calculated monthly subtotal sheets is:

(x

- *NM *2 )/ *N*

2

where

X

=

each score

M

=

mean score (average)

N

=

number of scores

S.D.

=

Standard Deviation

Example:

March 87

Grade2

Name

Grade

Able

3.041

9.247681

Baker

3.037

9.223369

Charles

3.052

9.314704

n=3

9.130

27.785754

X2

N

X

6 Month Mean/S.D.

X2

Month

n

X

Oct

4

12.189

37.143647

Nov

5

15.233

46.409231

Dec

7

21.333

65.016973

Jan

9

27.378

83.284956

Feb

12

36.651

111.944455

Mar

3

9.130

27.785754

TOTAL 40 121.914

371.585016

X2

N

X

(

)

371.585016 - 40 3.04785 2

=

40

(371.585016 - 371.5755849)/ 40 =

0.0002357775

NOTE: For this purpose, NATRACOM does not use the (N-1) form of

the standard deviation formula as an adjustment to allow

for sampling errors of a large population. The whole

population in question is used.

E-2

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