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46 CHAPTER 2 DESCRIPTIVE STATISTICS
We see that, since the mean and standard deviations are expressed in the same unit
of measurement, the unit of measurement cancels out in computing the coefficient of variation.
What we have, then, is a measure that is independent of the unit of measurement.
EXAMPLE 2.5.3
Suppose two samples of human males yield the following results:
Sample 1 Sample 2
Age 25 years 11 years
Mean weight 145 pounds 80 pounds
Standard deviation 10 pounds 10 pounds
We wish to know which is more variable, the weights of the 25-year-olds or the weights
of the 11-year-olds.
Solution:
A comparison of the standard deviations might lead one to conclude that
the two samples possess equal variability. If we compute the coefficients of
variation, however, we have for the 25-year-olds
and for the 11-year-olds
C.V. = 10 11002 = 6.9%
145
C.V. = 10 11002 = 12.5%
80
If we compare these results, we get quite a different impression. It is clear
from this example that variation is much higher in the sample of 11-yearolds
than in the sample of 25-year-olds.
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The coefficient of variation is also useful in comparing the results obtained by
different persons who are conducting investigations involving the same variable. Since
the coefficient of variation is independent of the scale of measurement, it is a useful
statistic for comparing the variability of two or more variables measured on different
scales. We could, for example, use the coefficient of variation to compare the variability
in weights of one sample of subjects whose weights are expressed in pounds with
the variability in weights of another sample of subjects whose weights are expressed in
kilograms.
Computer Analysis Computer software packages provide a variety of possibilities
in the calculation of descriptive measures. Figure 2.5.2 shows a printout of the
descriptive measures available from the MINITAB package. The data consist of the ages
from Example 2.4.2.
In the printout Q 1 and Q 3 are the first and third quartiles, respectively. These measures
are described later in this chapter. N stands for the number of data observations, and
N* stands for the number of missing values. The term SEMEAN stands for standard