Question

A simple random sample is taken from a population and yields the following data for a variable of the population:

find a point estimate for the population standard deviation (i.e., the standard deviation of the variable).

Short answer

The point estimate for the population standard deviation is$6.56$

Step-by-step solution

Step 1:Given Information 

Step 2:formulae used

The formula for sample standard deviation is given below:

$s=\sqrt{\frac{\sum {\left(x_i-\overline{x}\right)}^2}{n-1}}$

Step 3:Calculation 

Obtaining the sample standard deviation $\left(s\right)$

Calculating

width="79">∑xi-x2

Now,substituting 430 for $\sum _{}{\left(x_i-\overline{x}\right)}^2$and 11 for $n$in the samples of ariance formulae

$$\begin{gathered} s=\sqrt{\frac{430}{11-1}} \\ =\sqrt{\frac{430}{10}} \\ =\sqrt{43} \\ =6.56 \end{gathered}$$

The point estimate for the population standard deviation is$6.56$