Question

Calculate the standard deviation of the data set below.

(7, 9, 10, 11, 13)
The standard deviation is 4
The standard deviation is 2.
The standard deviation is 10.

Answer 1

Answer: 2

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}}`

`=(7+9+10+11+13)/(5)`

`=(50)/(5)`

= 10

So, the mean of data set is 10.

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

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

So, the standard deviation is 2.

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