Lecture 2 on Variance and Standard Deviation - Section 1.3 Variance and Standard Deviation Another important question we want to answer about data is

Lecture 2 on Variance and Standard Deviation - Section 1.3...

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Section 1.3 – Variance and Standard Deviation 1 Section 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: N x N i i 1 2 2 Population Standard Deviation: 2 where N is the number of values in our population, i x represents each data value in the population, and μ is the population mean. As stated above the standard deviation measures the same thing as the variance. Since we square the ) ( i x in the variance formula the units of x are squared, so to remedy this we take the square root.

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