Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# 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. - Mathematics

Sum

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.

#### Solution

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%

Concept: Coefficient of Variation
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