Question

Find the coefficient of variation of 24, 26, 33, 37, 29, 31.

Answer 1

Arrange in ascending order we get 24, 26, 29, 31, 33, 37

Assumed mean = 29

xi	di = xi − A = xi − 29	di2
24	− 5	25
26	− 3	9
29	0	0
31	2	4
33	4	16
37	8	64
`sumx_"i"` = 180	`sum"d"_"i"` = 6	`sum"d"_"i"^2` = 118

 Here n = 6, `sum"d"_"i"` = 6, `sum"d"_"i"^2` = 118

`bar(x) = (sumx_"i")/"n" = 180/6` = 30

⇒ `bar(x)` = 30

Standard deviation (σ) = `sqrt((sum"d"_"i"^2)/"n" - ((sum"d"_"i")/"n")^2`

= `sqrt(118/6 - (6/6)^2`

= `sqrt(19.666 - 1)`

= `sqrt(19.67 - 1)`

= `sqrt(18.67)`

(σ) = 4.32

Coefficent of variation = `sigma/(barx) xx 100`

= `4.32/30 xx 100`

= `432/30`

= 14.4

Coefficient of variation = 14.4%