MERITS AND DEMERITS OF MEDIAN Any descriptive statistic which summarizes the numerical data should have following four desirable properties: (i) It should be single valued. (ii) It should be algebraically calculable. (iii) It should consider every observed value. (iv) It should consider the frequency of every observed value. Note that mode does not satisfy any of these, while (arithmetic) mean possesses all these four desirable characteristics. Merits of median (i) Median satisfies two criteria of a good descriptive statistic: It is always single valued, and since the number of observations above the median equals the number of observations below there median, the median takes into account the frequency of all values in the distribution. (ii) Median is very useful in case of open-ended (e.g. Above 50 marks) classes since only the position and not the values of observations are required. (iii) It is easier to calculate the median than the mean in many cases. In some cases, median can be calculated just by inspection. (iv) The value of a median can be determined graphically whereas the value of the mean cannot be determined graphically. (v) Median is not affected by extreme values. For example, the median of 16, 20, 21, 22, 23, 24, 70 is 22 whereas the mean is 28. Here median is a more satisfactory measure of central tendency than the mean, which is easily swayed by extreme values. Demerits of median (i) Though the median considers the frequency of all observations, it does so only for counting purpose and does not really consider their magnitude. For example, the following two distributions, though very different, have same median, M=100. X 70 75 80 85 90 92 100 107 112 116 f (Group 1) 0 0 0 1 2 2 1 2 2 1 f (Group 2) 1 2 2 0 0 0 1 2 2 1 (ii) Most serious defect of median is that it is no algebraic. Though the formula for median involves only arithmetic operations of addition, subtraction, multiplication and division, we have to arrange the data in ascending order before applying the formula. Sorting the data in ascending or descending order involves logical comparisons ( or ) which take a lot of time when the number of observations is large. (ii)The value of the median is affected more by sampling fluctuations than the value of the mean. (iv)In some cases (e.g. When in a discrete series, the number of observations is even), the median is determined approximately as the mid-point of the two middle terms, while the mean can be calculated exactly. (v) If we know the medians of two or more sets of data, we can not calculate the median of the combined set, though the mean of a combined set can be calculated if means of individual sets are known. This happens because the median requires logical comparisons between individual items, rather than only algebraic treatment (i.e. Arithmetical calculations).