Question

Prove that the relation between mean median and mode is Mode = 3 median - 2 mean

Answer 1

A distribution in which the values of mean, median and mode coincide (i.e. mean = median = mode) is known as a symmetrical distribution. Conversely, when values of mean, median and mode are not equal the distribution is known as asymmetrical or skewed distribution. In moderately skewed or asymmetrical distribution a very important relationship exists among these three measures of central tendency. In such distributions the distance between the mean and median is about one-third of the distance between the mean and mode, as will be clear from the diagrams 1 and 2. Karl Pearson expressed this relationship as: 

Mode = mean - 3 [mean - median] 

Mode = 3 median - 2 mean 

and Median = mode + 2/3[mean-mode] 

Knowing any two values, the third can be computed.