Standard deviation
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This article/section deals with mathematical concepts appropriate for late high school or early college. |
Standard deviation is a measure for how much a set of values varies. It allows for one to find how likely it is for a specific value to be obtained by doing a Z-test.
Standard Deviation
The standard deviation of a set of values is a measure of how widely the values differ from each other. Specifically, standard deviation follows the equation:
This is the square root of the variance, which is:
Where:
is the arithmetic mean of all values of x
is the summation function
is the number of 
values
If the distribution of the values is normal then it follows the Empirical rule, which states that:
- For a more detailed treatment, see Empirical rule.
- 68% of the values will fall within 1
of the mean. - 95% of all values will fall within 2 of the mean.
- 99.7% of all values will fall within 3 of the mean.
