Standard Deviation Math Example 1

Solution

1. 1
   Compute the mean: $\bar{x} = \frac{2+4+4+4+5+5+7+9}{8} = \frac{40}{8} = 5$.
2. 2
   Find each squared deviation: $(2-5)^2 = 9$, $(4-5)^2 = 1$ (three times), $(5-5)^2 = 0$ (twice), $(7-5)^2 = 4$, $(9-5)^2 = 16$.
3. 3
   Sum of squared deviations: $9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32$.
4. 4
   Variance: $\sigma^2 = \frac{32}{8} = 4$.
5. 5
   Standard deviation: $\sigma = \sqrt{4} = 2$.