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Standard Deviation (continued)

All of these distributions have the same mean (62%) but you can see that they differ greatly. The difference lies in their spread. Set A is the most spread out, while C is the most clustered. One way of quantifying this spread is with the standard deviation, which is denoted with s.

To calculate the standard deviation, first find for each point, square the results, add them, divide by n-1, and finally take the square root. The formula is:

As you can see, the farther points are from the mean, the larger the standard deviation will be.

The standard deviation is a statistic calculated from a set of data. However, the term can also refer to the parameter that describes the spread of the data in the whole population. We sometimes use "population standard deviation" and the Greek letter s to distinguish this parameter from the "sample standard deviation" statistic, which is denoted with s.