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7
Appendix
The standard deviation
The standard deviation is designed to measure the amount of variation
in a set of data: the larger the standard deviation, the more variation
there is. Its calculation involves the following steps:
(1) Calculate the mean of the observations.
(2) Subtract the mean from each observation. The resulting values are
known as deviations.
(3) Square the deviations.
(4) Sum the squared deviations.
(5) Divide this sum by the number of observations.
(6) Find the square root of the figure derived in (5).
Example
The profits resulting from five products are shown below. Find the
standard deviation.
$18 000 $19 000 $19 000 $21 000 $18 000
The mean profit is $19 000, so we have:
Profit ($) Profit–mean (Profit–mean) 2
18 000 −1000 1 million
19 000 0 0
19 000 0 0
21 000 2000 4 million
18 000 −1000 1 million
Sum 6 million