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.