Find the missing frequencies in the following frequency distribution whose mean is $50$ and total frequency is $150$ .
$x$ $10$ $30$ $50$ $70$ $90$ $T o t a l$
$f$ $17$ $f_{1}$ $32$ $f_{2}$ $19$ $120$

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Solution

$x i$ $f i$ $f i x i$
$10$ $17$ $170$
$30$ $f 1$ $30 f 1$
$50$ $32$ $1600$
$70$ $f 2$ $70 f 2$
$90$ $19$ $1710$
$\sum f i = 68 + f_{1} + f_{2}$ $\sum f i x i = 3480 + 30 f_{1} + 70 f_{2}$
Given
$\sum f i = 150$

or, $68 + f_{1} + f_{2} = 150 \Rightarrow f_{1} + f_{2} = 82 - - - (1)$

$\frac{\sum f i x i}{\sum f i} = 50$

or, $\frac{3480 + 30 f_{1} + 70 f_{2}}{150} = 50$

or, $750 = 348 + 3 f_{1} + 7 f_{2} \Rightarrow 3 f_{1} + 7 f_{2} = 402 - - - (2)$

$\frac{3 f_{1} + 3 f_{2} = 246 3 f_{1} + 7 f_{2} = 420 - - -}{- 4 f_{2} = - 156 \Rightarrow f_{2} = 39}$

$∴$ From $(1)$ $f_{1} = 82 - 39$

$∴ f_{1} = 43$

So, the using frequencies are:

$f_{1} = 43$ and $f_{2} = 39$

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50

$x$ :	$10$	$30$	$50$	$70$	$90$
$f$ :	$17$	$f_{1}$	$32$	$f_{2}$	$19$	Total: $120$

Find the missing frequencies in the following frequency distribution, whose mean is $50$ .

x:	10	30	50	70	90
f:	17	f₁	32	f₂	19

Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is $50$ .

$\begin{matrix} x_{i} & f_{i} 10 & 17 30 & f_{1} 50 & 32 70 & f_{2} 90 & 19 Total & 120 \end{matrix}$

f_{1}

f_{2}

N = 100

32

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$T o t a l$
Frequency	$10$	$f_{1}$	$25$	$30$	$f_{2}$	$10$	$100$

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