In this article we will discuss about the relationship between mean, median and mode.
Distribution of statistical data shows how often the values in the data set occur. A distribution is said to be symmetrical when the values of mean, median and mode are equal. That is, there is equal number of values on both sides of the mean which means the values occur at regular frequencies.
In a histogram that is constructed for a data that is normally distributed, the columns would form a symmetrical bell shape, as shown below in Figure 14.1.
The graph drawn on such a data is known as a ‘normal curve’ or a ‘bell curve’ and appears as shown below in Figure 14.2.
When the values of mean, median and mode are not equal, then the distribution is said to be asymmetrical or skewed. A skewed distribution can either be positively skewed or negatively skewed. Histograms in case of skewed distribution would be as shown below in Figure 14.3.
In a positively skewed distribution, the median and mode would be to the left of the mean. That means that the mean is greater than the median and the median is greater than the mode (Mean > Median > Mode) (Fig. 14.4).
Whereas the negatively skewed distribution the median and the mode would be to the right of the mean. That means that the mean is less than the median and the median is less than the mode (Mean < Median < Mode) (Fig. 14.5).
Empirical studies have proved that in a distribution that is moderately skewed, a very important relationship exists between the mean, median and the mode. The distance between the mean and the median is about one-third the distance between the mean and the mode.
This relationship has been expressed by Karl Pearson in the following formula: