Median example (Grouped data):

 

Let’s consider the following frequency distribution that shows the exam scored receive by 40 students in a certain class:


Exam Score (xi)

 (fi)

CF

51-60

9

9

61-70

7

16

71-80

15

31

81-90

6

37

90-100

3

40


Here, n= 40.

Therefore, n/2 = 40/2 = 20

Thus, the observations lie between the class interval 61-70, which is called the median class.

Therefore,

Lower class limit = 61

Class size, h = 10

Frequency of the median class, f = 7

Cumulative frequency of the class preceding the median class, CF = 16.

Now, substituting the values in the median formula given above, we get

Median= 61 + (20-16)/7 *10 = 66.71

Therefore, the median marks for the given data are 66.71.



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