Question

The following data gives the distribution of total monthly household expenditure of $200$ families of a village. find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:

Expenditure(in Rs)	Number of families
1000-1500	24
1500-2000	40
2000-2500	33
2500-3000	28
3000-3500	30
3500-4000	22
4000-4500	16
4500-5000	7

Answer 1

$\Rightarrow$ Here, in given table we can see $1500-2000$ has highest frequency $40$.

$\therefore$ Modal class $=1500-2000$

$\Rightarrow$ So, $l=1500,f_1=40,f_0=24,f_2=33$ and $h=2000-1500=500$

$Mode=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$

$=1500+\frac{40-24}{2\left(40\right)-24-33}\times 500$

$=1500+\frac{16}{80-57}\times 500$

$=1500+\frac{16}{23}\times 500$

$=1500+347.826$

$=1847.83$

$\therefore$ Modal monthly expenditure of families is $Rs.1847.83$

$Class-Interval$	$f_i$	$Class-mark$ $x_i$	$f_i{x}_i$
$1000-1500$	$24$	$1250$	$30000$
$1500-2000$	$40$	$1750$	$70000$
$2000-2500$	$33$	$2250$	$74250$
$2500-3000$	$28$	$2750$	$77000$
$3000-3500$	$30$	$3250$	$97500$
$3500-4000$	$22$	$3750$	$82500$
$4000-4500$	$16$	$4250$	$68000$
$4500-5000$	$7$	$4750$	$33250$
	$\sum f_i=200$		$\sum f_i{x}_i=532500$

$\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}$

$=\frac{532500}{200}$

$=2662.5$

$\therefore$ Mean expenditure is $Rs.2662.5$