Standard Dev

#582 / Prob & Stats Medium

In a stress testing lab, a procedure was performed that produced the following results: 0, 1, 2, 3, 4, 5, 6, and 3. 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:

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

First, let’s calculate the mean:

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

$$$\mu=\frac{0+1+2+3+4+5+6+3}{8}=\frac{24}{8}=3$$$

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.

$$$\sigma =\sqrt{\frac{(0-3)^{2}+(1-3)^{2}+(2-3)^{2}+2(3-3)^{2}+(4-3)^{2}+(5-3)^{2}+(6-3)^{2}}{8}}$$$

$$$=\sqrt{\frac{(-3)^{2}+(-2)^{2}+(-1)^{2}+2(0)^{2}+(1)^{2}+(2)^{2}+(3)^{2}}{8}}$$$

$$$=\sqrt{\frac{9+4+1+0+1+4+9}{8}}=\sqrt{\frac{28}{8}}=\sqrt{3.5}=1.87$$$

1.87

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