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Question
Find the various and S.D. for the following set of numbers.
65, 77, 81, 98, 100, 80, 129
Solution
| xi | xi – `bar"x"` | `("x"_"i"− bar"x")^2` |
| 65 | – 25 | 625 |
| 77 | – 13 | 169 |
| 81 | – 9 | 81 |
| 98 | 8 | 64 |
| 100 | 10 | 100 |
| 80 | – 10 | 100 |
| 129 | 39 | 1521 |
| `∑"x"_"i"` = 630 | `∑("x"_"i"-bar"x")^2` = 2660 |
Here, n = 7
`bar"x"=(∑"x"_"i")/"n"=630/7` = 90
Var (X) = `sigma_"x"^2=1/"n"∑("x"_"i"-bar"x")^2=2660/7` = 380
∴ S.D.= `sigma_"x"`
= `sqrt("Var"(X)`
= `sqrt(380)`
= `2sqrt95`
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