Question

Calculate the standard deviation of the data set below.

Answer 1

Answer: 2

Step-by-step explanation:

Answer 2

Option 2

ANSWER:  

The Standard deviation of (7, 9, 10, 11, 13) is 2.

SOLUTION:

Given, data set is (7, 9, 10, 11, 13)

Standard deviation $\sigma=\sqrt{\frac{\Sigma(\mathrm{xi}-\mu) 2}{n}}$

Where, $\mathrm{x}_{\mathrm{i}}$ is element of data set

$\mu$  is mean of data set

n is total number observations.

Now, mean $\mu=\frac{\text {sum of observations}}{\text {number of observations}}$

$=\frac{7+9+10+11+13}{5}$

$=\frac{50}{5}$

= 10

So, the mean of data set is 10.

Now, standard deviation $\sigma=\sqrt{\frac{(7-10) 2+(9-10) 2+(10-10) 2+(11-10) 2+(13-10) 2}{5}}$

$\begin{array}{l}{\sigma=\sqrt{\frac{(-3) 2+(-1) 2+(0) 2+(1) 2+(3) 2}{5}}} \\ {\sigma=\sqrt{\frac{9+1+1+9}{5}}} \\ {\sigma=\sqrt{\frac{20}{5}}} \\ {\sigma=2}\end{array}$

So, the standard deviation is 2.

Hence, the second option is right, i.e. standard deviation is 2.