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
	$\sum f_i=120$			$\sum f_i{u}_i=-37$	$\sum f_i{u_i}^2=275$

​​$\overline{X}=a+h\left(\frac{\sum f_i{u}_i}{N}\right)=3450+700\left(\frac{-37}{120}\right)=3234.17$

$$\begin{gathered} {\sigma }^2=h^2\left[\frac{\sum f_i{u_i}^2}{N}-{\left(\frac{\sum f_i{u}_i}{N}\right)}^2\right]=490000\left[\frac{275}{120}-\frac{1369}{14400}\right]=1076332.64 \\ \sigma =\sqrt{1076332.64}=1037.46 \\ CV=\frac{\sigma }{\overline{X}}\times 100=\frac{1037.46}{3234.17}\times 100=32.08 \end{gathered}$$