CNATRAINST 1500.4F
18 May 1999
ALTERNATE METHOD FOR COMPUTING STANDARD DEVIATION
The general formula for the standard deviation is:
S.D. = d 2 / N
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
S.D. =
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
M =X /N
Nov
5
15.233
46.409231
M = 121.914 / 40 = 3.04785
Dec
7
21.333
65.016973
Jan
9
27.378
83.284956
X 2 - NM 2
Feb
12
36.651
111.944455
S.D. =
Mar
3
9.130
27.785754
N
TOTAL 40 121.914
371.585016
X2
N
X
(
)
X 2 - NM 2
371.585016 - 40 3.04785 2
S.D. =
=
40
N
(371.585016 - 371.5755849)/ 40 =
S.D. =
0.0002357775
S.D. = 0.015355
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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