Having discussed mean, median and mode, we now turn to the relationship amongst these three measures of central tendency. We shall discuss the relationship assuming that there is a unimodal frequency distribution.
When a distribution is symmetrical, the mean, median and mode are the same, as is shown below in the following
In case, a distribution is skewed to the right, then mean> median> mode. Generally, income distribution is skewed to the right where a large number of families have relatively low income and a small number of families have extremely high income. In such a case, the mean is pulled up by the extreme high incomes and the relation among these three measures is as shown in Here, we find that mean> median> mode.
When a distribution is skewed to the left, then mode> median> This is because here mean is pulled down below the median by extremely low values.
This is shown as in the figure.
Given the mean and median of a unimodal distribution, we can determine whether it is skewed to the right or left. When mean> median, it is skewed to the right; when median> mean, it is skewed to the left. It may be noted that the median is always in the middle between mean and mode.
