Relation Between Mean, Median and Mode

Mean, median, and mode are three different ways of finding the central value of data. When the data is fairly symmetrical, these three values lie close to each other. When the data is skewed or uneven, their positions shift.

Understanding how they are related helps in estimating one measure when the other two are known, especially in situations where calculating mode directly is difficult.

For many types of data that are not perfectly symmetrical but not extremely skewed either, there is a simple approximate relationship between mean, median, and mode. This is called the empirical formula.

The relationship is:

This formula is not exact for all data sets, but it works well for moderately skewed distributions. It helps estimate the mode when only mean and median are known.

In a perfectly symmetrical distribution, mean, median, and mode are equal. But when the data is stretched more on one side, these values move away from each other. The empirical formula shows how far mode lies from mean and median based on the shape of the data.

The idea is that the median lies between mean and mode in many practical data sets.

Suppose the mean of a data set is 20 and the median is 18. To estimate the mode:

So, the approximate mode is 14.

This shows how the formula helps when the mode is not directly visible from the data.