Find the missing frequencies x and y if the mean of the following distribution is 51.75 and the sum of missing frequencies is 80. Class 0-10 10-20 20-30 30-40 40-50 50-60 70-80 80-90 90-100 Frequencies 3 5 7 x 12 15 12 y 2 8

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Solution

Dear Student,

CLASS INTERVALS (f_i) (x_i) f_ix_i

0−10 3 5 15

10−20 5 15 75

20−30 7 25 175

30−40 x 35 35x

40−50 12 45 540

50−60 15 55 825

60−70 12 65 780

70−80 y 75 75y

80−90 2 85 170

90−100 8 95 760

Total
∑ f_i= 64+x+y ∑ f_ix_i=3325+35x+75y

$mean = 51.75 \Rightarrow \frac{3325 + 35 x + 75 y}{64 + x + y} = 51.75 \Rightarrow 67 x - 93 y = 52 . . . . (1) x + y = 80 . . . . (2) Multiply (2) by 93, we get 93 x + 93 y = 7440 . . . . (3) Adding (1) and (3), we get 160 x = 7492 \Rightarrow x = 46.825 Now, from (2), we get y = 33.175$

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