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