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प्रश्न
Answer the following :
Calculate coefficient of variation of the following data: 23, 27, 25, 28, 21, 14, 16, 12, 18, 16
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उत्तर
We construct the following table to compute C.V. :
| xi |
`x_"i" - bar(x)` `bar(x)` = 20 |
`(x_"i" - barx)^2` |
| 23 | 3 | 9 |
| 27 | 7 | 49 |
| 25 | 5 | 25 |
| 28 | 8 | 64 |
| 21 | 1 | 1 |
| 14 | – 6 | 36 |
| 16 | – 4 | 16 |
| 12 | – 8 | 64 |
| 18 | – 2 | 4 |
| 16 | – 4 | 16 |
| `sumx_"i"` = 200 | `sum(x_"i" - barx)^2` = 284 |
n = 10
`bar(x) = (sumx_"i")/"n" = 200/10` = 20
Variance (x) = `sigma_x^2`
= `(sum(x_"" - barx)^2)/"n" = 284/10` = 28.4
S.D. = `sigma_x = sqrt(28.4)` = 5.33
C.V. = `sigma_x/bar(x) xx 100`
= `5.33/20 xx100`
= 26.65
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