The median is also a measure of central tendency. Unlike arithmetic mean, this median is based on the position of a given observation in a series arranged in an ascending or descending order. Therefore, it is called a positional average. It has nothing to do with the magnitude of all the observations, as in the case of arithmetic mean. Simply, median refers to the middlemost value of the variable when they are arranged in order of magnitude. The position of the median in a series is such that an equal number of items lie on either side of it. Median of a given series is the value of the variable that divides the series-into two equal parts. It is the most central point of a series where half of the items lie above this value and the remaining half lie below this value. In the case of a frequency curve the median is that value of the variable which splits the area into two equal parts. The median is usually denoted by 'Md '. Canor defined the median as “The median is that value of the variable which divides the group in two equal parts, one part comprising all the values greater and other all values less than the median.
Merits and Limitations of Median
You have studied the meaning, methods of computation and properties of median. Now, let us discuss the merits and limitations of median.
Merits:
1) For an open-ended distribution, such as income distribution, the median gives a more representative value.
2) Since median is not distorted by the extreme items, in some cases it is preferred over mean as the latter is likely to be distorted by extreme values.
3) For dealing the qualitative phenomena, median is the most suitable average,
4) Since median minimises the total absolute deviations, median is preferred in the situations wherein the total geographical distance is to be minimised. For example, there is a conference of five tope executives from five different cities of India lying almost in a straight line. The city located at a median distance would be a more proper place for the conference.
5) While taking a decision to buy a particular brand of tyre, when only one or two tyres are to be bought, the brand with greater median run will be preferred. Similarly, in buying a washing machine, the machine with greater median life will be preferred, rather than one with a greater mean life.
Limitations:
1) Median is not capable of algebraic treatment. That means we cannot have a combined median of two or more groups, unless all the items of the groups are known.
2) It is described, sometimes, as an insensitive measure as it is not based on all items of the series.
3) It is affected more by sampling fluctuations than the value of mean.
4) The computational formula of a median is in a way an interpolation under the assumption that the items in the median class are uniformly distributed which is not very true.
5) The impression created by median in some cases may be illusory and deceptive because its value is determined strictly by the value of middle observations(s). For example, in lotteries the median value of the prize won by a ticket is always zero when all tickets are considered (more than 50% of the tickets will not get any prize). This median value of prize will not help in analysing the prizes offered by lotteries as the matter of interest may be the first prize out of a number of prizes offered.
