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

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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.

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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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APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 10th SSLC Mathematics Answers Guide
Chapter 8 Statistics and Probability
Exercise 8.2 | Q 6 | Page 316
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