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## Variance and Standard Deviation

### Definition

The variance of a series of numbers is the mean of all the squares of the differences between each number and the mean of all the numbers.

The standard deviation of a series of numbers is the square root of their variance.

The estimated standard deviation and estimated variance of a series of numbers are the best guesses for those measures when only a sample of the entire population of numbers is used as a proxy for all of them.

### How are they used?

The arithmetic mean (or simply mean) of a series of numbers is the average of the numbers as we normally understand it. If we have the following five numbers:

52, 53, 57, 58, 60

then their mean is:

The mean is useful, because it gives us an idea of the how ...

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