CNATRAINST 1500.4F
18 May 1999
APPENDIX E
STANDARD DEVIATIONS
The following definitions and examples will assist in
understanding the relationship between demonstrated performance
(academic tests, cumulative flight grade, etcetera) and group
distributions:
Mean - the arithmetic average of the group
Distribution - the range in grades from the best to worst
Variance - the mean (average) of the deviation squared
Standard Deviation - the average amount by which values
(grades/scores) deviate from the mean. The greater the
distribution, the bigger the deviations and the bigger the
standard ("average") deviation.
Standard Deviation = Square Root of the Variance.
Mean and Deviation Computations
A class of ten students had the following scores:
80
80
90
92
92
94
96
98
98
100
Mean =
80 + 80 + 90 + 92 + 92 + 94 + 96 + 98 + 98 + 100
10
Mean =
92.0
Deviation from 92.0-12
-12
-2
0
0
+2
+4
+6
+6
+8
Squared Deviation = 144
144
4
0
0
4
16
36
36
64
Mean of Deviation Squared =
144
144
4
0
0
4
16
36
36
64
10
Mean of Deviation Squared =
44.8
Variance =
44.8
Standard Deviation = Square Root of 44.8 = 6.69
2 X Standard Deviation = 2 X 6.69 = 13.38
-2 Standard Deviation = 92 - 13.38 = 78.62 or less
E-1
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