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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.
Sum
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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%
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