Empirical Relationship Between Mean, Median and Mode

Empirical Relationship Between Mean, Median and Mode

A distribution in which the value of mean, median and mode coincide, is know symmetrical and if these values are not equal, then the distribution is said asymmetrical or skewed.

In a moderately skewed distribution, there is a relation amongst mean, median and mode which is as follows.

Mean – Mode = 3 (Mean – Median)

Example 1: If in a frequency distribution the mean and median are 20 and 21 respectively, then its mode is approximately

Solution: Mean – Mode = 3 (Mean – Median)

20 – Mode = 3 (20 – 21)

20 – Mode = – 3

Mode = 23

Example 2: If the mode of the data is 18 and the mean is 24, then median is

Solution: Since, Mode = 3 (Median) – 2 (Mean)

18 = 3 (Median) – 2 (24)

Median = 22

Example 3: If in a moderately asymmetrical distribution mode and mean of the data are 6k and 9k respectively

Solution: Mode = 3 (Median) – 2 (Mean)

6k = 3 (Median) – 18k

Median = 8k