Q 8.9 - Elementary Statistics

Question

A simple randoes 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).

Step-by-Step Solution

Answer

The point estimate for the population standard deviation is 9.72

Step 1:Given Information

Step 2:Calculation

The mean of the variable is:

$$\begin{gathered} \overline{x}=\frac{\sum x^n}{n} \\ =\frac{9+32+37+32+20+24+10+15+21+30}{10} \\ =\frac{230}{10} \\ =23 \end{gathered}$$

Now,

The formula for sample standard deviation is given below:

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

Calculating 

$\sum {\left(x_i-\overline{x}\right)}^2$

Step 3:Calculation (b)

Substituting 850 for $\sum _{}{(x-\overline{x})}^2$

in the sampie standard deviation formulae

$$\begin{gathered} s=\sqrt{\frac{850}{10}} \\ =\sqrt{94,4444} \\ =9.72 \end{gathered}$$

Thus, the point estimate for the population standard deviation is 9.72