For the following sample, use the computational formula to calculate SS. Then, compute the sample variance and standard deviation. Scores: 1, 3, 1, 1
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S.No | X | (X-x̄) | (X-x̄)^{2} | |
1 | 1 | -0.500 | 0.25000 | |
2 | 3 | 1.500 | 2.25000 | |
3 | 1 | -0.500 | 0.25000 | |
4 | 1 | -0.500 | 0.25000 | |
Σx | 6 | Σ(X-x̄)^{2}= | 3.0000 | |
x̄=Σx/n | 1.500 | s^{2}=Σ(x-x̄)^{2}/(n-1)= | 1.00000 | |
s=√s^{2 } = | 1.0000 |
from above
SS =Σ(X-x̄)^{2}=3.00
sample variance s^{2} +SS/(n-1) =3/(4-1) =1
standard deviation s =√s^{2} =1
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