Question

if the samples are 16, 17, 15, 24, 20, 20, 20, 23, 18, and 19. what is the point estimate of the population standard deviation?

Answer 1

The sample standard deviation s is a point estimate of the population standard deviation σ:

$s=\sqrt{\cfrac{\sum{( x-\bar x)^2}}{n-1}};\\ \bar x=\\ =\cfrac{16+17+15+24+20+20+20+23+18+19}{10}=\\ =19.2;\\$

$X-\bar x=\\ =\begin{Bmatrix} 16-19.2, 17-19.2,15-19.2,...,19-19.2 \end{Bmatrix}=\\ =\begin{Bmatrix}-3.2,-2.2,-4.2,...,-0.2\end{Bmatrix};$

$\sum{( x-\bar x)^2}=(-3.2)^2+(-2.2)^2+(-4.2)^2+...+\\ +(-0.2)^2=73.6;\\ s=\sqrt{\cfrac{73.6}{10-1}}=2.86.$