The sample variance and sample standard deviation
:
s
2
s
The sample variance
s
2
and the sample standard deviation
s
provide an important measures of variation or
spread in a set of data. The sample variance, loosely speaking, is the “average” squared distance from a data
value (say
y
i
) to the sample average
¯
y
of all data values; that is, the sample variance
s
2
=
∑
n
i
=1
(
y
i

¯
y
)
2
n

1
is an average of the squared deviation across all values
y
1
,y
2
,...,y
n
in the data set. (Recall
¯
y
again may be
used as a measure of the central or typical value of the data, so with
(
y
i

¯
y
)
2
we access how spread the value
y
i
is away from the center of the data
¯
y
). The more distant data values are from the sample mean
¯
y
of the data,
the larger the sample variance
s
2
and the large the sample standard deviation
s
=
√
s
2
.
You should have learned how to compute the standard deviation of a set of numbers in your introductory
statistics class. In case you have forgotten or never learned, the example below shows how to compute the
standard deviation of a small data set. Usually we use a computer to ﬁnd standard deviations, but you should
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 Spring '11
 elizabeth
 Standard Deviation, Variance, Sample standard deviation

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