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Question
Answer the following :
Find variance and S.D. for the following set of numbers: 125, 130, 150, 165, 190, 195, 210, 230, 245, 260
Solution
| xi | `x_"i" - barx` | `(x_"i" - barx)^2` |
| 125 | – 65 | 4225 |
| 130 | – 60 | 3600 |
| 150 | – 40 | 1600 |
| 165 | – 25 | 625 |
| 190 | 0 | 0 |
| 195 | 5 | 25 |
| 210 | 20 | 400 |
| 230 | 40 | 1600 |
| 245 | 55 | 3025 |
| 260 | 70 | 4900 |
| `sumx_"i"` = 1900 | `sum(x_"i" - barx)^2` = 20000 |
Here, n = 10
`bar(x) = (sumx_"i")/"n" = 1900/10` = 190
Var (X) = `sigma_x^2 = 1/"n" sum(x_"i" - barx)^2 = 20000/10` = 2000
S.D. = `sigma_x = sqrt("Var(X)")`
= `sqrt(2000)`
= 44.72
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