Question

The table below
shows the daily expenditure on food of 30 households in a locality

Daily expenditure (in Rs.)	$100-150$	$150-200$	$200-250$	$250-300$	$300-350$
No. of households	$6$	$7$	$12$	$3$	$2$

Find the mean and the median daily expenditure on food.

Answer 1

$C.I.$	$Mid-value$ $x_i$	$f_i$	$c.f.$	$x_i{f}_i$
$100-150$	$125$	$6$	$6$	$750$
$150-200$	$175$	$7$	$13$	$1225$
$200-250$	$225$	$12$	$25$	$2700$
$250-300$	$275$	$3$	$28$	$825$
$300-350$	$325$	$2$	$30$	$650$
		$\sum f_i=30$		$\sum f_i{x}_i=6150$

We know that, $Mean\left(\overline{x}\right)=\frac{\sum f_i{x}_i}{\sum f_i}$

$\therefore \text{mean expenditure on food}=\frac{6150}{30}=205$

We also know that, $Median=l+\frac{\frac{n}{2}-c.f}{f}\times h$

$n=\sum f_i=30$, then $\frac{n}{2}=\frac{30}{2}=15$

$\therefore$ Median class $=200-250$

Then, $l=200,c.f=13,f=12$ and $h=50$

$\therefore \text{median expenditure on food}=200+\frac{15-13}{12}\times 50$

$=200+8.33$

$\therefore$ $Median=208.33$

Hence, the mean and median expenditure on food are $205$ and $208.33$, respectively.