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

$x$:	10	30	50	70	90
$f$:	17	$f_1$	32	$f_2$	19	Total 120.

Given:

The arithmetic mean of the given data is 50.

To do:

We have to find the missing frequencies in the given frequency distribution.

Solution:

  $68+f_1+f_2 =120$

$\Rightarrow f_1+f_2=120-68=52$

$\Rightarrow f_1=52-f_2$...........(i)

We know that,
Mean$=\frac{\sum fx}{\sum f}$ 

Mean $50=\frac{3480+30f_1+70f_2}{68+f_1+f_2}$ 

$50(120)=3480+30f_1+70f_2$

$3480+30f_1+70f_2=6000$

$30(52-f_2)+70f_2=6000-3480$          [From (i)]

$1560-30f_2+70f_2=2520$

$40f_2=2520-1560$

$f_2=\frac{960}{40}$

$f_2=24$

$\Rightarrow f_1=52-24=28$

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Updated on: 10-Oct-2022

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