**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