Question

If mean of the following frequency distribution is $1.46$ then find the unknown frequency.

x:	0	1	2	3	4	5	Total
f:	46	...	...	25	10	5	200

• A. $38$ and $76$
• B. $35$ and $72$
• C. $38$ and $71$
• D. $32$ and $72$

Answer 1

The correct option is A $38$ and $76$

$x_i$	$f_i$	$f_i{x}_i$
$0$	$46$	$0$
$1$	$x$	$x$
$2$	$y$	$2y$
$3$	$25$	$75$
$4$	$10$	$40$
$5$	$5$	$25$
	$\sum f_i=x+y+86$	$\sum f_i{x}_i=140+x+2y$

$Mean=1.46$ [ Given ]

We know, $N=200$ [ Given ]

So, $x+y+86=200$

$\therefore$ $x+y=114$ ------ ( 1 )

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

$\Rightarrow$ $1.46=\frac{140+x+2y}{200}$

$\Rightarrow$ $292=x+2y+140$

$\Rightarrow$ $x+2y=152$ ----- ( 2 )

Subtracting equation ( 1 ) from ( 2 ) we get,

$y=38$

Now, $x+38=114$

$\therefore$ $x=76$

$\therefore$ The unknown frequencies are $38$ and $76$.