Question

The time taken (in minutes) to complete a homework by 8 students in a day are given by 38, 40, 47, 44, 46, 43, 49, 53. Find the coefficient of variation.

Answer 1

Arrange in ascending order we get, 38, 40, 43, 44, 46, 47, 49, 53.

Assumed mean = 46

xi	di = xi − A = xi − 46	di2
38	− 8	64
40	− 6	36
43	− 3	9
44	− 2	4
46	0	0
47	1	1
49	3	9
53	7	49
`sumx_"i"` = 360	`sum"d"_"i"` = − 8	`sum"d"_"i"^2` = 172

Here n = 8, `sumx_"i"` = 360, `sum"d"_"i"` = − 8, `sum"d"_"i"^2` = 172

`bar(x) = (sumx_"i")/"n" = 360/8` = 45

⇒ `bar(x)` = 45

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

= `sqrt(172/8 - ((-8)/8)^2`

= `sqrt(21.5 - 1)`

= `sqrt(20.5)`

= 4.527

(σ) = 4.53

Coefficient of variation = `sigma/(barx) xx 100%` 

= `4.53/45 xx 100%` 

= `453/45%` 

= 10.066

Coefficient of variation = 10.07%