Question

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:$120$

Answer 1

Given frequency $=120$

$\Rightarrow 17+f_1+32+f_2+19=120$

$\Rightarrow f_1+f_2=52$

Mean =$\frac{\sum x_i{f}_i}{\sum f_i}$

$\Rightarrow$mean =$\frac{(10\times 17)+(30\times f1)+(50\times 32)+(72\times f2)+(90\times 19)}{120}$

$\Rightarrow$mean =$\frac{170+30f_1+1600+70f_2+1710}{120}=50$

$\Rightarrow 3f_1+7f_2=252$

$\Rightarrow 3f_1+7(52-f_1)=252$

$\Rightarrow f_1=28$

$\Rightarrow f_2=24$