## Population Standard Deviation

In a stress testing lab, a procedure was performed that produced the following results: 11, 11, 11, 11, 12, 13, 13, and 14. If the mean for these measurements is 12, what is the standard deviation?

##
__
__**Hint**

**Hint**

$$$\sigma =\sqrt{\frac{1}{N}\Sigma (X_{1}-\mu )^{2}}$$$

where
$$N$$
is the number of items or observations,
$$X$$
is the value from the set, and
$$\mu$$
is the mean.

##
__
__**Hint 2**

**Hint 2**

To find the mean:

$$$\mu=\frac{sum\:of\:terms}{number\:of\:terms}$$$

For population standard deviation (not to be confused with sample standard deviation):

$$$\sigma =\sqrt{\frac{1}{N}\Sigma (X_{1}-\mu )^{2}}$$$

where
$$N$$
is the number of items or observations,
$$X$$
is the value from the set, and
$$\mu$$
is the mean.

$$$\sigma =\sqrt{\frac{4(11-12)^{2}+1(12-12)^{2}+2(13-12)^{2}+1(14-12)^{2}}{8}}$$$

$$$\sigma =\sqrt{\frac{4+0+2+4}{8}}=1.118$$$

1.118