Locate the missing frequency, if arithmetic mean of the following series is 44.8.

X 20 30 40 50 60 70

f 5 ? 15 10 8 5

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Solution

X f fX

20
30
40
50
60
70 5
f
15
10
8
5 100
30f
600
500
480
350

$Σ f$ =43 + f $Σ f X$ =2030 + 30f

Let missing frequency be f

Given:
Mean, $X = 44.8$

We know,

$X = \frac{Σ f X}{Σ f} o r, 44.8 = \frac{2030 + 30 f}{43 + f} o r, 1926.4 + 44.8 f = 2030 + 30 f o r, 14.8 f = 103.6 \Rightarrow f = \frac{103.6}{14.8} = 7$

Hence, the missing frequency is 7

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