The following data are from a simple random sample 5, 8, 10, 7, 10, 14

The point estimate of the population variance is

8

Population Variance = \(\sum_{i=1}^{n}\frac{(x_i-\overline{x})^2}{n-1}=σ^2 \)

$\overline{x}=\frac{5+8+10+7+10+14}{6}=\frac{54}{6}=9$

$σ^2=\frac{(5-9)^2+(8-9)^2(10-9)^2(7-9)^2(10-9)^2(14-9)^2}{6}$

$σ^2=\frac{16+1+1+4+1+25}{6}=\frac{48}{6}=8$