Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th
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Find the coefficient of variation of 24, 26, 33, 37, 29, 31. - Mathematics

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Sum

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

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Solution

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%

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 5 | Page 316
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