Question

Calculate the population variance of the heights of trees(in meters)

10.1, 10.2, 12.4, 3.6,14.3,15.9,16.17

Answer 1

$$mean=\bar{x}=\dfrac{1}{n}\sum_ix_i=\dfrac{1}{7}(10.1+10.2$$

$$+ 12.4+ 3.6+14.3+15.9+16.17)$$

$$=\dfrac{82.67}{7}=11.81$$

$$Var(X)=\sigma^2=\dfrac{1}{n}\sum_i(x_i-\bar{x})^2$$

$$=\dfrac{1}{7}((10.1-11.81)^2+(10.2-11.81)^2$$

$$+(12.4-11.81)^2+(3.6-11.81)^2$$

$$+(14.3-11.81)^2+(15.9-11.81)^2$$

$$+(16.17-11.81)^2)=\dfrac{115.2062}{7}\approx16.4580$$