Question

Calculate the mean and S.D. for the following data:

Expenditure in Rs:	0-10	10-20	20-30	30-40	40-50
Frequency:	14	13	27	21	15

Answer 1

Expenditure (Rs)	$f_i$	Midpoint $\left(x_i\right)$	$f_i{x}_i$	$x_i-\overline{X}$	${\left(x_i-\overline{X}\right)}^2$	$f_i{\left(x_i-\overline{X}\right)}^2$
0−10	14	5	70	$-$21.1	445.21	6233.94
10−20	13	15	195	$-$11.1	123.21	1601.73
20−30	27	25	675	$-$1.1	1.21	34.67
30−40	21	35	735	8.9	79.21	1663.41
40−50	15	45	675	18.9	357.21	5358.15
	$\sum f_i=90$		$\sum f_i{x}_i=2350$			$\sum f_i{\left(x_i-\overline{X}\right)}^2=14891.9$

Mean, $\overline{X}=\frac{2350}{90}=26.11$
Variance, ${\sigma }^2=\frac{14891.9}{90}=165.47$

$SD,\sigma =\sqrt{165.47}=12.86$