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Chapter 3: Measures of Variability
3-5
The Variance and Standard Deviation
The variance and the standard deviation are the most common and useful
measures of variability. These two measures provide information about how
the data vary about the mean.
If the data is clustered around the mean, then the variance and the standard
deviation will be somewhat small. If the data is widely dispersed around the
mean, then the variance and the standard deviation will be somewhat large.
Figure 3-12
illustrates with the dot plots for two data sets. The means are
the same for these data sets. Observe that Data A is spread out much more
about the mean than Data B and so one would expect that the variance and
the standard deviation to be much larger than the variance and standard
deviation for Data B about the same mean.
Figure 3-12:
Dot plot display used to illustrate variance
and standard deviation