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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