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How to Calculate Statistics from

## How to Calculate Statistics from ## how to calculate data

The value of calculating data is in the data. That’s because the importance of data often comes from the decisions we make with the data.

### data

The procedure to calculate the standard deviation depends on whether the numbers are the entire population or are data from a sample. The calculations are similar, but not identical. Therefore the symbol used to represent the standard deviation depends on whether it is calculated from a population or a sample. The lower case letter [latex]s[/latex] represents the sample standard deviation and the Greek letter [latex]σ[/latex] (sigma, lower case) represents the population standard deviation. If the sample has the same characteristics as the population, then [latex]s[/latex] should be a good estimate of [latex]σ[/latex]. The deviations show how spread out the data are about the mean. The data value [latex]11.5[/latex] is farther from the mean than is the data value [latex]11[/latex] which is indicated by the deviations [latex]0.97[/latex] and [latex]0.47[/latex]. A positive deviation occurs when the data value is greater than the mean, whereas a negative deviation occurs when the data value is less than the mean. The deviation is [latex]–1.525[/latex] for the data value nine. If you add the deviations, the sum is always zero. (For Example 1, there are [latex]n = 20[/latex] deviations.) So you cannot simply add the deviations to get the spread of the data. By squaring the deviations, you make them positive numbers, and the sum will also be positive. The variance, then, is the average squared deviation. (Source: courses.lumenlearning.com)

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