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?
Expand 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
Time Analysis
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