Coefficient of variation: The coefficient of variation (CV) is the SD divided by the mean. For
the DBP example,
percent.
Range
The range of a set of values is the minimum value subtracted from the maximum value:
Consider the example from the preceding section, where you had DBP measurements from seven study
participants (which were 84, 84, 89, 91, 110, 114, and 116 mmHg). The minimum value is 84, the
maximum value is 116, and the range is 32 (equal to
).
Centiles
The basic idea of the median is that ½ (half) of your numbers are less than the median, and the other ½
are greater than the median. This concept can be extended to other fractions besides ½.
A centile (also referred to as percentile) is a value that a certain percentage of the values are
less than. For example, ¼ of the values are less than the 25th centile (and ¾ of the values are
greater). The median is just the 50th centile. The 25th, 50th, and 75th centiles are called the first,
second, and third quartiles, respectively, and are used often. There are other sets of centiles, such
as deciles, which break at every ten percentiles, that are used less often.
As we explain in the earlier section “Median,” if the sorted sequence of your numerical variable has
no middle value, you have to calculate the median as the average of the two middle numbers. The same
situation comes up in calculating centiles, but there are different ways that statistical software does the
calculation. Fortunately, the different formulas they use give nearly the same result.
The inter-quartile range (IQR) is the difference between the 25th and 75th centiles (the first
and third quartiles).
Numerically expressing the symmetry and shape of the distribution
In the following sections, we discuss two summary statistics used to describe aspects of the symmetry
and shape of the distribution of values of numerical variables (pictured earlier in Figure 9-2).
Skewness
Skewness refers to the left-right symmetry of the distribution. Figure 9-3 illustrates some examples.