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Question
Find variance and S.D. for the following set of numbers.
25, 21, 23, 29, 27, 22, 28, 23, 27, 25
(Given `sqrt(6.6)` = 2.57)
Solution
We prepare the following table for the calculation of variance and S.D.:
| xi | `"x"_"i" - bar"x"` | `("x"_"i" - bar"x")^2` |
| 25 | 0 | 0 |
| 21 | – 4 | 16 |
| 23 | – 2 | 4 |
| 29 | 4 | 16 |
| 27 | 2 | 4 |
| 22 | – 3 | 9 |
| 28 | 3 | 9 |
| 23 | – 2 | 4 |
| 27 | 2 | 4 |
| 25 | 0 | 0 |
| `sum"x"_"i"` = 250 | `sum("x"_"i" - bar"x")^2` = 66 |
Here, n = 10
`bar"x" = (sum"x"_"i")/"n" = 250/10` = 25
Var (X) = `sigma_"x"^2 = 1/"n" sum("x"_"i" - bar"x")^2`
= `1/10 xx 66`
= 6.6
∴ S.D. = `sigma_"x"`
= `sqrt("Var (X)")`
= `sqrt(6.6)`
= 2.57
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