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प्रश्न
Calculate coefficient of variation of marks secured by a student in the exam, where the marks are: 85, 91, 96, 88, 98, 82
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उत्तर
| xi | `x_"i" - bar(x)` | `(x_"i" - barx)^2` |
| 85 | – 5 | 25 |
| 91 | 1 | 1 |
| 96 | 6 | 36 |
| 88 | – 2 | 4 |
| 98 | 8 | 64 |
| 82 | – 8 | 64 |
| `sumx_"i"` = 540 | `sum(x_"i" - barx)^2` = 194 |
Here, n = 6, `bar(x) = (sumx_"i")/"n" = 540/6` = 90
Var(X) = `sigma_x^2 = 1/"n" sum(x_"i" - barx)^2 = 194/6` = 32.33
∴ S.D. = `sigma_x = sqrt("Var(X)")`
= `sqrt(32.33)`
= 5.69
Now, C.V. = `100 xx sigma_x/bar(x)`
= `100 xx (5.69)/90`
= 6.32%
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