Question

Calculate coefficient of variation from the following data:

Income (in Rs):	1000-1700	1700-2400	2400-3100	3100-3800	3800-4500	4500-5200
No. of families:	12	18	20	25	35	10

Answer 1

Income (Rs)	\[f_i\]	Midpoint \[\left( x_i \right)\]	\[u_i = \frac{x_i - 3450}{700}\]	\[f_i u_i\]	\[f_i {u_i}^2\]
1000−1700	12	1350	−3	−36	108
1700−2400	18	2050	−2	−36	72
2400−3100	20	2750	−1	−20	20
3100−3800	25	3450	0	0	0
3800−4500	35	4150	1	35	35
4500−5200	10	4850	2	20	40
	\[\sum f_i = 120\]			\[\sum f_i u_i= 37\]	\[\sum f_i {u_i}^2 = 275\]

\[\bar{X} = a + h\left( \frac{\sum f_i u_i}{N} \right) = 3450 + 700\left( \frac{- 37}{120} \right) = 3234 . 17\]

\[\sigma^2 = h^2 \left[ \frac{\sum f_i {u_i}^2}{N} - \left( \frac{\sum f_i u_i}{N} \right)^2 \right] = 490000\left[ \frac{275}{120} - \frac{1369}{14400} \right] = 1076332 . 64\]
\[\sigma = \sqrt{1076332 . 64} = 1037 . 46\]
\[CV = \frac{\sigma}{\bar{X}} \times 100 = \frac{1037 . 46}{3234 . 17} \times 100 = 32 . 08\]