Question

Compute the following:a. Sample meanb. Sample variancec. Sample standard deviation

Answer 1

Given:

Here a table given in the question.

Required:

a.Sample mean

b.Sample variance

c.Sample standard deviation

Explanation:

a.Sample mean

$\frac{\sum_^x_i}{n}$

is the formula to find the sample mean

$\frac{2+4+6+8+10+8+6+5+1}{9}=5.56=x$

b.Sample variance

$\frac{\sum_^(x_i-x)^2}{n-1}=S^2$

is the formula to find the sample variance

$\begin{gathered} \sum_^(x_i-x)^2=(2-5.56)^2+(4-5.56)^2+(6-5.56)^2+(8-5.56)^2+ \\ (10-5.56)^2+(8-5.56)^2+(6-5.56)^2+(5-5.56)^2+(1-5.56)^2 \\ \text{ =12.6736+2.4336+0.193+5.954+19.714+5.954+0.3136+20.793} \end{gathered}$$\sum_^(x_i-x)^2=68.03$

now put in formula

$S^2=\frac{\sum_^(x_i-x)^2}{n-1}=\frac{68.03}{10-1}=\frac{68.03}{9}=7.56$

and S is the sample standard deviation

$S=\sqrt[]{7.56}=2.75$

Final Answer:

a.Sample mean=5.56

b.Sample variance=7.56

c.Sample standard deviation=2.75