Question

Find the missing frequencies in the following frequency distribution whose mean is $34$.

$x$	$10$	$20$	$30$	$40$	$50$	$60$	$Total$
$f$	$4$	$f_2$	$8$	$f_1$	$3$	$4$	$35$

Answer 1

$x_i$	$f_i$	$x_i{f}_i$
$10$	$4$	$40$
$20$	$f_2$	$20f_2$
$30$	$8$	$240$
$40$	$f_1$	$40f_1$
$50$	$3$	$150$
$60$	$4$	$240$

$\sum f_i=35$

$\sum f_i{x}_i=670+20f_2+40f_1$

$mean=\frac{\sum f_i{x}_i}{\sum f_i}\Rightarrow 34=\frac{670+20f_2+40f_1}{35}$

Or, $1190=670+20f_2+40f_1$

Or, $40f_1+20f_2=520$

Or, $2f_1+f_2=26$ ....... $\left(1\right)$

Also, $\Sigma f_i=19+f_1+f_2=35\Rightarrow f_1+f_2=16$ ........ $\left(2\right)$

Subtracting (2) from (1) we get,

$f_1=10$

From eq.(2) we get,

$f_2=16-10=6$