91Ó°ÊÓ

The data points are as follows:

21,54,9,45,51.

A data set's range is given by range = max-min.

Range

$$\begin{gathered} =54-9 \\ =45 \end{gathered}$$

As a result, the data set's range is 45.

The data points are as follows:

21,54,9,45,51.

A data set's range is given by range = max-min.

The formula computes the standard deviation.

$s=\sqrt{\frac{\underset{}{∑}{x_i}^2-{\left(\underset{}{∑}{x}_i\right)}^2/n}{n-1}}$

Determine the mean of the given data set.

$$\begin{gathered} \stackrel{¯}{x}=\frac{21+54+45+9+51+}{5} \\ \stackrel{¯}{x}=\frac{180}{5} \\ \stackrel{¯}{x}=36 \end{gathered}$$

$$\begin{gathered} s=\sqrt{\frac{{\left(21-36\right)}^2+{\left(54-36\right)}^2+{\left(45-36\right)}^2+{\left(9-36\right)}^2+{\left(51-36\right)}^2}{5-1}} \\ s≈19.8997 \end{gathered}$$

As a result, the required value is 19.8997

The data points are as follows:

21,54,9,45,51.

A data set's range is given by range = max-min.

The formula computes the standard deviation.

$$\begin{gathered} s=\sqrt{\frac{\underset{}{∑}{x_i}^2-{\left(\underset{}{∑}{x}_i\right)}^2/n}{n-1}} \\ s=\sqrt{\frac{8064-{\left(180\right)}^2/5}{5-1}} \\ s≈19.8997 \end{gathered}$$

As a result, the required value is 19.8997

Because the formula does not matter when calculating the standard deviation, the answers in parts (a) and (b) are the same.