Question

Answer the following :

Calculate coefficient of variation for the data given below:

Income (Rs.)	3000 - 4000	4000 - 5000	5000 - 6000	6000 - 7000	7000 - 8000	8000 - 9000	9000 - 10000
No. of families	24	13	15	28	12	8	10

Answer 1

We construct the following table to compute C.V. :

C.I.	Mid-value xi	fi	ui = `(x_"i" - "A")/"h"` A = 6500, h = 1000	fiui	fiui2 = fiui × ui
3000 - 4000	3500	24	– 3	– 72	216
4000 - 5000	4500	13	– 2	– 26	52
5000 - 6000	5500	15	– 1	– 15	15
6000 - 7000	6500	28	0	0	0
7000 - 8000	7500	12	1	12	12
8000 - 9000	8500	8	2	16	32
9000 - 10000	9500	10	3	30	90
		`sumf_"i"` = 110	–	`sumf_"i"u_"i"` = –55	`sumf_"i"u_"i"^2` = 417

From the table,

`sumf_"i"` = 110, `sumf_"i"u_"i"` = −55, `sumf_"i"u_"i"^2` = 417

∴ `bar(u) = (sumf_"i"u_"i")/(sumf_"i") = (-55)/110` = – 0.5

∴ `bar(x) = "A" + "h"bar(u)` = 6500 + 1000(– 0.5) = 6000

`sigma_u^2 = (sumf_"i"u_"i"^2)/(sumf_"i") - (baru)^2`

= `417/110 − (-0.5)^2`

= 3.791 − 0.25

= 3.541

∴ `sigma_u sqrt(3.541)` = 1.882

∴ `sigma_x = "h"sigma_x` = 1000 × 1.882 = 1882

C.V. = `sigma_x/bar(x) xx 100`

= `1882/6000 xx 100`

 = 31.36