91Ó°ÊÓ

The data points are as follows:

3, 3, 3, 3, 3, 3

A data set's range is given by range = max-min = 0.

Standard deviation is the measure of deviation in data. As there is no variation in the data because the values of all the data points are the same (one can verify that using range).

As a result, the data set's standard deviation is 0.

The data points are as follows:

3, 3, 3, 3, 3, 3

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.

$$\begin{gathered} \stackrel{¯}{x}=\frac{3+3+3+3+3+3}{6} \\ \stackrel{¯}{x}=\frac{18}{6} \\ \stackrel{¯}{x}=3 \end{gathered}$$

$$\begin{gathered} s=\sqrt{\frac{{\left(3-3\right)}^2+{\left(3-3\right)}^2+{\left(3-3\right)}^2+{\left(3-3\right)}^2+{\left(3-3\right)}^2{\left(3-3\right)}^2}{6-1}} \\ s=0 \end{gathered}$$

As a result, the required value is 0.

The data points are as follows:

3, 3, 3, 3, 3, 3

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

The formula computes the standard deviation.

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

Standard deviation is zero if all observations in a data set are equal.

As a result, the data set's standard deviation is 0.

The data points are as follows:

3, 3, 3, 3, 3, 3

We can observe that the standard deviation is zero because all the observations are the same.

So, if a data set's sample standard deviation is zero, all observations in the data set are equal.