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Question

# Calculate the median from the following frequency distribution: Class5âˆ’1010âˆ’1515âˆ’2020âˆ’2525âˆ’3030âˆ’3535âˆ’4040âˆ’45Frequency5615105422

A

16.5
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B

17.5
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C

18.5
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D

19.5
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Solution

## The correct option is D 19.5We 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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