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Standard Deviation
Simply put, the standard deviation tells us how far a typical member of a sample or population is from the mean value of that sample or population. A large standard deviation suggests that a typical member is far away from the mean. A small standard deviation suggests that members are clustered closely around the mean.
It is calculated by taking the square root of the variance.
Here are the six basic steps to calculate the standard deviation.
Given this list of numbers:
1, 3, 4, 5, 6, 7, 9
1. Calculate the mean.
1 + 3 + 4 + 5 + 6 + 7 + 9 = 35 / 7 = 5
2. Subtract the mean from all values in the list.
-4, -2, -1, 0, 1, 2, 4
3. Square the numbers (squaring a negative number removes the minus sign).
16, 4, 1, 0, 1, 4, 16
4. Add these numbers.
16 + 4 + 1 + 0 + 1 + 4 + 16 = 42
5. Divide this number by the number of items in the list (the result is the variance).
42 / 7 = 6
6. Finally, square root the variance to get the standard deviation.
(Roughly 2.45)