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