Question

Compute the missing frequencies $f_1$ and $f_2$ in the following data if the mean is $166\frac{9}{26}$ and the sum of the frequencies is $52$

C.I	140-150	150-160	160-170	170-180	180-190	190-200	Total
Freq.	5	$f_1$	20	$f_2$	$6$	$2$	$52$

Answer 1

$Class-Interval$	$Class-Mark$ $x_i$	$f_i$	$f_i{x}_i$
$140-150$	$145$	$5$	$725$
$150-160$	$155$	$f_1$	$155f_1$
$160-170$	$165$	$20$	$3300$
$170-180$	$175$	$f_2$	$175f_2$
$180-190$	$185$	$6$	$1110$
$190-200$	$195$	$2$	$390$
		$\sum f_i=33+f_1+f_2$	$\sum f_i{x}_i=5525+155f_1+175f_2$

$\Rightarrow$ $\sum f_i=52$ [ Given ]

$\Rightarrow$ $33+f_1+f_2=52$

$\therefore$ $f_1+f_2=19$

$\therefore$ $f_1=19-f_2$ ----- ( 1 )

$\Rightarrow$ $Mean=\frac{\sum f_i{x}_i}{\sum f_i}$

$\Rightarrow$ $166\frac{9}{26}=\frac{5525+155f_1+175f_2}{52}$

$\Rightarrow$ $\frac{4325}{26}\times 52=5525+155(19-f_2)+175f_2$

$\Rightarrow$ $8650=5525+2945-155f_2+175f_2$

$\Rightarrow$ $180=20f_2$

$\therefore$ $f_2=9$

$\Rightarrow$ $f_1=19-9=10$

$\therefore$ $f_1=10$ and $f_2=9$