Question

The mean of the following frequency distribution is 62.8 and the sum of all frequencies is 50. Compute the missing frequencies $f_1$ and $f_2$.

Class	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120	Total
Frequency	5	$f_1$	10	$f_2$	7	8	50

Answer 1

Given mean of frequency distribution is $62.8$

& the sum of all frequencies is $50$

Class	mid point of class $\left(x_i\right)$	frequency $\left(f_i\right)$	$f_i{x}_i$
$0-20$ $20-40$ $40-60$ $60-80$ $80-100$ $100-120$	$10$ $30$ $50$ $70$ $90$ $110$	$5$ $f_1$ $10$ $f_2$ $7$ $8$	$50$ $30f_1$ $500$ $70f_2$ $630$ $880$
		$50$	$2060+30f_1+70f_2$

$\therefore \sum f_i=50$

$30+f_1+f_2=50\Rightarrow f_1+f_2=50-30=20$

$f_1+f_2=20$ ___(1)

mean $\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{2060+30f_1+70f_2}{50}$

$62.8\times 50=2060+30f_1+70f_2$

$30f_1+70f_2=3140-2060=1080$

$10(3f_1+7f_2)=1080$

$3f_1+7f_2=108$ __(2)

$f_1=9\Rightarrow \left(1\right)\Rightarrow f_2=20-f_1=20-9$

$f_2=11$

$\therefore f_1=9,f_2=11$