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Question
Calculate coefficient of variation of marks secured by a student in the exam, where the marks are: 2, 4, 6, 8, 10.
(Given: `sqrt8` = 2.8284)
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Solution
| xi | `bb("x"_"i"-bar"x")` | `bb(("x"_"i"-bar"x"))^2` |
| 2 | −4 | 16 |
| 4 | −2 | 4 |
| 6 | 0 | 0 |
| 8 | 2 | 4 |
| 10 | 4 | 16 |
| `∑bb"x"_"i"` = 30 | `∑bb("x"_"i"-bar"x")^2` = 40 |
Here, n = 5
`bar"x" = (sum"x"_"i")/"n"`
= `(30)/(5)`
= 6
Var(X) = `sigma_"x"^2` = `1/"n"sum("x"_"i"-bar"x")^2`
= `40/5`
= 8
∴ S.D. = σx = `sqrt("Var"("X")) =sqrt8` = 2.8284
Now, C.V. = `sigma/bar"x"xx100`
= `(2.8284)/(6) xx 100`
= 47.14%
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