9/11/20129Variance and Standard DeviationWhy do we square the deviations?The sum of the squared deviations of any set of observations from their mean is the smallest that the sum of squared deviations from any number can possibly be.The sum of the deviations of any set of observations from their mean is always zero.Why do we emphasize the standard deviation rather than the variance? s, not s2, is the natural measure of spread for Normal distributions.shas the same unit of measurement as the original observations.Why do we average by dividing by n −1 rather than n in calculating the variance?The sum of the deviations is always zero, so only n−1 of the squared deviations can vary freely.The number n−1 is called the degrees of freedom.Properties of Standard Deviationsmeasures spread about the mean and should be used only when the mean is the measure of center.s= 0 only when all observations have the same value and there is no spread. Otherwise, s> 0.sis not resistant to outliers. shas the same units of measurement as the original observations. Choosing among summary statisticsBecause the meanis not resistant to outliers or skew, use it to describe distributions that are fairly symmetrical and don’t have outliers.