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Question

The mean of the following data is 42, find the missing frequencies x and y if the sum of the frequencies is 100.
Class interval 0−10 10−20 20−30 30−40 40−50 50−60 60−70 70−80
Frequency 7 10 x 13 y 10 14 9

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Solution

The given data is shown as follows:
Class interval Frequency (fi) Class mark (xi) fixi
0−10 7 5 35
10−20 10 15 150
20−30 x 25 25x
30−40 13 35 455
40−50 y 45 45y
50−60 10 55 550
60−70 14 65 910
70−80 9 75 675
Total ∑ fi = 63 + x + y ∑ fixi = 2775 + 25x + 45y

Sum of the frequencies = 100

ifi=10063+x+y=100x+y=100-63x+y=37y=37-x ....(1)

Now, The mean of given data is given by

x¯=ifixiifi42=2775+25x+45y1004200=2775+25x+45y4200-2775=25x+45y1425=25x+45(37-x) from (1)1425=25x+1665-45x20x=1665-142520x=240x=12

If x = 12, then y = 37 − 12 = 25

​Thus, the value of x is 12 and y is 25.

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