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प्रश्न
Compute variance and standard deviation for the following data:
| x | 2 | 4 | 6 | 8 | 10 |
| f | 5 | 4 | 3 | 2 | 1 |
उत्तर
We prepare the following table for the calculation of variance and S.D.:
| xi | fi | fixi | fixi2 |
| 2 | 5 | 10 | 20 |
| 4 | 4 | 16 | 64 |
| 6 | 3 | 18 | 108 |
| 8 | 2 | 16 | 128 |
| 10 | 1 | 10 | 100 |
| Total | N = 15 | ∑fixi = 70 | ∑fixi2 = 420 |
`bar"x"=(sum"f"_"i""x"_"i")/"N"=70/15` = 4.6667
Var(X) = `σ_"x"^2=(sum"f"_"i""x"_"i"^2)/"N"-(bar"x")^2`
= `(420)/(15) - (4.6667)^2`
= 28 – 21.7781
= 6.2219
∴ S.D. = `sigma_"x" = sqrt("Var"("X"))=sqrt6.2219`
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