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Mean

Find the miss...

Question

Find the missing frequencies if the mean of the given data is $53$ .
Age in years $0 - 20$ $20 - 40$ $40 - 60$ $60 - 80$ $80 - 100$ Total
Number of People $15$ $F_{1}$ $21$ $F_{2}$ $17$ $100$

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Solution

$15 + F_{1} + 21 + F_{2} + 17 = 100$

$15 + F_{1} + 21 + F_{2} + 17 \Rightarrow F_{1} + F_{2} = 47 . . . (i)$

$\frac{15 \times 10 + 30 \times F_{1} + 50 \times 21 + 70 \times F_{2} + 90 \times 17}{250} = 53$

$150 + 30 F_{1} + 1050 + 70 F_{2} + 1530 = 131250 . . . (i i)$

on solving (1) & (2)

$F_{1} = 180.75 F_{2} = - 227.75$

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