Question

The table below shows the daily expenditure on the food of $25$ households in a locality. Find the mean daily expenditure on food by a suitable method.

Daily expenditure(in c)	100-150	150-200	200-250	250-300	300-350
Number of households	4	5	12	2	2

Answer 1

Step 1: Form a required table to find mean.

To determine the midpoint of the given interval using the formula.

Midpoint ($x_i$) $=$ $\left(\frac{upperlimit+lowerlimit}{2}\right)$

Let us assume the mean ($A$) $=$$225$

Class size ($h$) $=$$50$

Class Interval	Number of households ($f_i$)	Mid-point ($x_i$)	$d_i=x_i-A$	$u_i=\frac{d_i}{50}$	$f_i{u}_i$
$100-150$	$4$	$125$	$-100$	$-2$	$-8$
$150-200$	$5$	$175$	$-50$	$-1$	$-5$
$200-250$	$12$	$225$	$0$	$0$	$0$
$250-300$	$2$	$275$	$50$	$1$	$2$
$300-350$	$2$	$325$	$100$	$2$	$4$
	$\sum _{}^{}{f}_i=25$				$\sum _{}^{}{f}_i{u}_i=-7$

Step 2: Find mean.

The mean formula is

Mean, ${\displaystyle \stackrel{-}{x}}=A+\left({\displaystyle \frac{\sum _{}^{}{f}_i{u}_i}{\sum _{}^{}{f}_i}}\right)\times h$

So, ${\displaystyle \stackrel{-}{x}}=225+\left({\displaystyle \frac{-7}{25}}\right)\times 50$

${\displaystyle \stackrel{-}{x}}=225-14$

${\displaystyle \stackrel{-}{x}}=211$

Therefore, the mean daily expenditure on food is $211$