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Question

Find the median from the following data:
MarksNo. of studentsBelow 1012Below 2032Below 3057Below 4080Below 5092Below 60116Below 70164Below 80200

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Solution

Sol:

The given series is of inclusive form. Converting it into exclusive form and preparing the cumulative frequency table, we get

Marks Frequency fi C.F
0-10 12 12
10-20 20 32
20-30 25 57
30-40 23 80
40-50 12 92
50-60 24 116
60-70 24 116
70-80 36 200
N=∑fi=200

N =200

=> N/2 = 100

Now,

The cumulative frequency just greater than 100 is 116 and corresponding class is 50-60.

Thus, the median class is 50-60

I = 50, h = 10, f = 24, c = C.F. preceding median class = 92 and N/2 = 100

Median = I+[h×(N/2−c)/f]=50+[10×(100−92)/24]

=50+[10×84/24]=50+[10×84/24]

= 50 + 3.33 = 53.33

Hence, Median = 53.33


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