Standard Deviation Math Example 2

Solution

1. 1
   Compute the sample mean: $\bar{x} = \frac{10+12+23+23+16+23+21+16}{8} = \frac{144}{8} = 18$.
2. 2
   Squared deviations: $(10-18)^2=64$, $(12-18)^2=36$, $(23-18)^2=25$ (three times), $(16-18)^2=4$ (twice), $(21-18)^2=9$.
3. 3
   Sum: $64 + 36 + 25 + 25 + 4 + 25 + 9 + 4 = 192$.
4. 4
   Sample variance (divide by $n-1 = 7$): $s^2 = \frac{192}{7} \approx 27.43$.
5. 5
   Sample standard deviation: $s = \sqrt{27.43} \approx 5.24$.