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Question
Find the various and S.D. for the following set of numbers.
7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 8, 2, 6
Solution
Given data: 7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 2, 6
The tabulated form of the above data is as given below:
| xi | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 11 |
| fi | 3 | 2 | 1 | 1 | 3 | 2 | 3 | 1 | 2 |
We prepare the following table for the calculation of variance and S.D.
| xi | fi | fixi | fixi2 |
| 2 | 3 | 6 | 12 |
| 3 | 2 | 6 | 18 |
| 4 | 1 | 4 | 16 |
| 5 | 1 | 5 | 25 |
| 6 | 3 | 18 | 108 |
| 7 | 2 | 14 | 98 |
| 8 | 3 | 24 | 192 |
| 9 | 1 | 9 | 81 |
| 11 | 2 | 22 | 242 |
| Total | N = 18 | ∑fixi = 108 | ∑fixi2 = 792 |
`bar"x"= (sum"f"_"i""x"_"i")/"N"`
= `108/18`
= 6
var (X) = `σ_"x"^2=(sum"f"_"i""x"_"i"^2)/"N"-(bar"x")^2`
= `792/18-(6)^2`
= 44 – 36
= 8
∴ S.D. `sigma_x = sqrt("Var"("X")`
= `sqrt(8)`
= `2sqrt(2)`
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