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Question
Compute variance and standard deviation for the following data:
| x | 2 | 4 | 6 | 8 | 10 |
| f | 5 | 4 | 3 | 2 | 1 |
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Solution
We prepare the following table for the calculation of variance and S.D.:
| x | f | fx | x2 | fx2 |
| 2 | 5 | 10 | 4 | 20 |
| 4 | 4 | 16 | 16 | 64 |
| 6 | 3 | 18 | 36 | 108 |
| 8 | 2 | 16 | 64 | 128 |
| 10 | 1 | 10 | 100 | 100 |
| Total | 15 | 70 | - | 420 |
`bar"x"=(sum"fx")/"N"`
= `70/15`
= 4.6667
`bar"x"` = 4.67
Var(X) = `σ^2`
= `"L"/"N"(sum"fx"^2)-(bar"x")^2`
= `(1)/(15)xx420 - (4.67)^2`
= `140/5-21.8089`
= 28 – 21.8089
= 6.1911
∴ S.D. = `sigma_"x"`
= `sqrt("Var"("X"))`
= `sqrt6.1911`
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