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

xpenditure(Rs)	\[f_i\]	Midpoint \[\left( x_i \right)\]	\[f_i x_i\]	\[f_i x_i\]	\[\left( x_i - \bar{X} \right)^2\]	\[ f \left ( x_i - \bar{X} \right)^2\]
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
	\[\sum f_i = 90\]		\[\sum f_i x_i = 2350\]			\[\sum f_i \left( x_i - \bar{X} \right)^2 = 14891 . 9\]

Mean,

\[\bar{X} = \frac{2350}{90} = 26 . 11\]

Variance,

\[\sigma^2 = \frac{14891 . 9}{90} = 165 . 47\]

\[SD, \sigma = \sqrt{165 . 47} = 12 . 86\]