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MEDIAN

(a)For the observations x1, x2, ….., x the median is the middle value if the number of observations is odd and have been arranged in ascending or descending order of magnitude. For even number of observations the median is taken as the average of two middle values after they are arranged in ascending or descending order of magnitude. e.g., For the data, 10, 17, 15, 25, 18, let us arrange them in ascending order as 10, 15, 17, 18 and 25. Here the middle value is 17. Hence the median is 17. Consider another sets of data, 21, 40, 19, 28, 33 30. Let us arrange them in ascending order as 19, 21, 28, 30, 33 and 40. There are two middle values 28 and 30. So the median is (28 + 30)/2 i.e., 29.

(b) For simple frequency distribution the median is detained by using less than cumulative frequency distribution. Here the median is that value of the variable for which the cumulative frequency is just greater than  where N = total frequency.

e.g. consider

Here N = 30, N/2= 15. So the cumulative frequency just greater than 15 is 18 and the corresponding variable value is 20. Then the median is 20.

 

(a)For grouped frequency distribution, the median is obtained by the following :

Where,

L = Lower limit or boundary of the median class.

h = Width of the class interval

f = Frequency of the median class.

N = Total frequency

C = Cumulative frequency of the class preceding the median class.

Example 4. Find the median of the following data:

Solution.  

Note. In case of unequal class-intervals median is sometimes preferred to A.M.