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Question

Calculate the median from the following frequency distribution:
Class5101015152020252530303535404045Frequency5615105422

A

17.5
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B

16.5
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C

18.5
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D

19.5
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Solution

The correct option is D
19.5

We prepare the cumulative frequency table, as shown:

Class fi cfi
5-10 5 5
10-15 6 11
15-20 15 26
20-25 10 36
25-30 5 41
30-35 4 45
35-40 2 47
40-45 2 49
Σfi = 49

N = Σfi = 49

⇒ N/2 = 24.5

The cumulative frequency greater than 24.5 is 26 and the corresponding class is 15-20.

Thus the median class is 15-20.

Therefore, l= 15, h = 5,
f = 15,
c.f. of preceding class = 11 and N/2 = 24.5

Median,
M = l + ((N/2 − cf)/f) × h

Median = 15 + ((24.5 – 11)/15) × 5

Median = 15 + 4.5

Median = 19.5

Hence, median is 19.5 .


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