Elementary Statistics (1+1)

6.3.2 Merits and Demerits of Median

Merits:

i) It is rigidly defined

ii) It is easily understood and is easy to calculate. In some cases it can be located merely by inspection.

iii) It is not at all affected by extreme values

iv) It can be calculated for distributions with open-end classes.

Demerits:

i) In case of even number of observations median cannot be determined exactly. We merely estimate it by taking the mean of the two middle most terms.

ii) It is not based on all the observations. For example, the median of 10, 25, 50, 60 and 65 is 50. We can replace the observations 10 and 25 by any two values which are smaller than 50 and the observations 60 and 65 by any two values greater than 50, without affecting the value of median. This property is sometimes described by saying that median is insensitive.

iii) It is not amenable to algebraic treatment

iv) As compared with mean, it is affected much by fluctuations of sampling.

Uses:

i) Median is the only average to be used while dealing with qualitative data which cannot be measured quantitatively but still can be arranged in ascending or descending order of magnitude, e.g. to find the average intelligence or average honesty among a group of people.

ii) It is to be used for determining the typical value in problems concerning wages, distribution of wealth, etc.