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Calculate the Missing Frequency from the Following Distribution, It Being Given that the Median of the Distribution is 24. - CBSE Class 10 - Mathematics

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Question

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

Age in years 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
No. of persons 5 25 ? 18 7

Solution

Class interval Frequency Cumulative frequency
0 - 10 5 5
10 - 20 25 30
20 - 30 x 30 + x
30 - 40 18 48 + x
40 - 50 7 55 + x
  N = 55 + x  

Given

Median = 24

Then median class = 20 - 30

l = 20, h = 30 - 20 = 10, F = 30 and f = x

Median `=l+{(N/2-F)/f}xxh`

`24=20+((55+x)/2-30)/x xx10`

`24 - 20=((55+x)/2-30)/x xx10`

`4x=((55+x)/2-30)xx10`

`4x xx2=(55 + x -60)xx10`

8x = 550 + 10x - 600

10x - 8x = 600 - 550

2x = 50

x = 25

∴ Missing frequency = 25

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Solution Calculate the Missing Frequency from the Following Distribution, It Being Given that the Median of the Distribution is 24. Concept: Median of Grouped Data.
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