Using the computational formula for the sample, the SS is 37.50, the variance is 5.36, and the standard deviation is 2.31.
How do we compute the standard deviation using the computational formula?
The computational formula is given as follows:
SS = Sum of Squares = ΣX^2 - ((ΣX)^2 / n) ………………………. (1)
X = each value
n = number of values = 8
Therefore, we have:
ΣX^2 = 14^2 + 20^2 + 17^2 + 16^2 + 12^2 + 16^2 + 15^2 + 16^2 = 2,022
(ΣX)^2 = (14 + 20 + 17 + 16 + 12 + 16 + 15 + 16)^2 = 15,876
Substituting all the values into equation (1), we have:
SS = 2,022 - (15,876 / 8) = 37.50
Variance = S^2 = SS / (n – 1) = 37.50 / (8 – 1) = 5.35714285714286, or 5.36
Standard deviation = S = Variance^0.5 = 5.35714285714286^0.5 = 2.31
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