Question

for the data set 6, 5, 10, 11, 13, the mean, $\bar{x}$, is 9. what is the standard deviation?
the formula for the sample standard deviation is $s = sqrt{\frac{1}{n - 1}sum(x - \bar{x})^2}$.
use the table to help you.

$x$	$x-\bar{x}$	$(x - \bar{x})^2$
5	-4	16
10	1	1
11	2	4
13	4	16
sum =		46

round your answer to the nearest tenth.
a. 9.2
b. 11.25
c. 3.4
d. 3

Explanation:

Step1: Identify values

We have $n = 5$ (number of data - points), and $\sum(x-\bar{x})^2=46$.

Step2: Apply standard - deviation formula

The formula for the sample standard deviation is $s=\sqrt{\frac{1}{n - 1}\sum(x-\bar{x})^2}$. Substitute $n = 5$ and $\sum(x-\bar{x})^2 = 46$ into the formula:
\[

$$\begin{align*} s&=\sqrt{\frac{46}{5 - 1}}\\ &=\sqrt{\frac{46}{4}}\\ &=\sqrt{11.5}\\ &\approx3.4 \end{align*}$$

\]

Answer:

C. 3.4