Question

The mean of the following frequency distribution is $350$, find the missing frequency

Class	$100-200$	$200-300$	$300-400$	$400-500$	$500-600$	$600-700$
Frequency	$5$	$3$	$3$	-	$2$	$1$

Answer 1

Class-Interval	Frequency($f_i$)	Midpoint($x_i$)	$f_i{x}_i$
$100-200$	$5$	$150$	$750$
$200-300$	$3$	$250$	$750$
$300-400$	$3$	$350$	$1050$
$400-500$	$x$	$450$	$450x$
$500-600$	$2$	$550$	$1100$
$600-700$	$1$	$650$	$650$

From the above table,

$\sum f_i=14+x$

and $\sum f_i{x}_i=4300+450x$

Let the missing frequency be ${}^{\prime }{x}^{\prime }$.
Mean, $\overline{x}=350$
We know that,
$\therefore \overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}$
$\therefore 350=\frac{4300+450x}{14+x}$
$\therefore 4900+350x=4300+450x$
$\therefore 600=100x$
$\therefore x=\frac{600}{100}=6$
Hence, the missing frequency $=6$