120 PART 3 Getting Down and Dirty with Data
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» Coefficient of variation: The coefficient of variation (CV) is the SD divided by
the mean. For the DBP example, CV
14.4 / 98.3 0.1465, or 14.65 percent.
Range
The range of a set of values is the minimum value subtracted from the maximum
value:
Range maximum value minimum value
Consider the example from the preceding section, where you had DBP measure-
ments 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 116
84
).
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 vari-
ables (pictured earlier in Figure 9-2).