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Section 1.3 – Variance and Standard Deviation 1Section 1.3 Variance and Standard Deviation Another important question we want to answer about data is about its spread or dispersion. If the outcomes cover a wide range, the spread is larger. If the outcomes are clustered around a single value, the spread is smaller. The spread is zero if all values are equal. The population variance,2(read sigma-squared), is the average of the squared differences of the data values from the mean. The population standard deviation, , is the square root of the population variance. Population Variance: NxNii122Population Standard Deviation: 2where N is the number of values in our population, ixrepresents each data value in the population, and μis the population mean. As stated above the standard deviation measures the same thing as the variance. Since we square the )(ixin the variance formula the units of x are squared, so to remedy this we take the square root.