Answer to Question #328717 in Statistics and Probability for Tenshi

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:

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

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

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