The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

46 CHAPTER 3 Graphics and Summary Statistics

The mean, median, and mode may all be different in the bimodal case.

In the symmetric bimodal case, the mean and median may be the same,

but neither of the two modes would equal the median (one will be

below and the other above both the mean and the median).

For symmetric unimodal distributions: mean = median = mode.

For unimodal distributions that are right skewed: mean < median <

mode. For unimodal distributions that are left skewed:

mean > median > mode. Although the mode can sometimes be a good

measure of central tendency, at least in the case of the symmetric

bimodal distribution, the natural center is in the “ middle ” between the

two modes at where there is a trough. That middle of the valley between

the peaks is where the median and mean are located.

3.8 MEASURES OF DISPERSION

Measures of dispersion or spread (also called variability) that we

discuss in this section are:

Figure 3.7. Example of a unimodal and a bimodal distribution. * The bimodal
distribution in the picture has two peaks but the peak to the right is the mode because it is
the highest peak.

(a) Unimodal Distribution (b) Bimodal Distribution

x-Variable x-Variable

Frequency Frequency

* In the example above, we chose a symmetric unimodal distribution and an asymmetric

bimodal distribution. Unimodal distributions can also be skewed and bimodal distributions

symmetric.