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प्रश्न
Compute variance and standard deviation for the following data:
| X | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
| F | 8 | 10 | 10 | 7 | 6 | 4 | 3 | 4 | 2 | 6 |
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उत्तर
| xi | fi | fixi | fixi2 |
| 2 | 8 | 16 | 32 |
| 4 | 10 | 40 | 160 |
| 6 | 10 | 60 | 360 |
| 8 | 7 | 56 | 448 |
| 10 | 6 | 60 | 600 |
| 12 | 4 | 48 | 576 |
| 14 | 3 | 42 | 588 |
| 16 | 4 | 64 | 1024 |
| 18 | 2 | 36 | 648 |
| 20 | 6 | 120 | 2400 |
| N = 60 | `sumf_"i"x_"i"` = 542 | `sumf_"i"x_"i"^2` = 6836 |
`bar(x) = (sumf_"i"x_"i")/"N" = 542/60` = 9.03
Var (X) = `sigma_x^2 = (sumf_"i"x_"i"^2)/"N" - (barx)^2`
= `6836/60 - (9.03)^2`
= 113.93 – 81.54
= 32.39
∴ S.D. = `sigma_x = sqrt("Var(X)")`
= `sqrt(32.39)`
= 5.69
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