## 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
$$\sigma =\sqrt{\frac{1}{N}\Sigma (X_{1}-\mu )^{2}}$$$where $$N$$ is the number of items or observations, $$X$$ is the value from the set, and $$\mu$$ is the mean. Hint 2 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