4.6 Empirical Relation Between Mean, Median And Mode
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 onethird 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 +
Knowing any two values, the third can be computed.
Example
Given median = 20.6, mode = 26 Find mean.
Solution:
Click here to enlarge
**********

Index
4.1 Introduction
4.2 Arithmetic Mean
4.3 Properties of Arithmetic Mean 4.4 Median
4.5 Mode
4.6 Empirical relation between mean, median & mode
Chapter 5
