6.3 Standard Deviation and zScores Variance and Standard Deviation Sometimes we want to find out how far the data values in a data set are from the middle of a data set. In that case, we can find the variance or standard deviation. x is the data value, μ is the mean and N is the population size, and n is the sample size. Population Variance σ2 = ∑ (x−μ)2 N Sample Variance s2 = ∑ (x− xˉ)2 n−1 Population Standard Deviation σ= ∑ (x−μ)2 N = ∑ x2 −N ∗μ2 N Sample Standard Deviation s= (∑ (x− xˉ2 ) n−1 = ∑ x2 −n∗xˉ2 n−1 z-Scores When we have the standard deviation, we can describe how far data values are from the mean by determining how many standard deviations they are from the mean. This is knows the z-score. The more standard deviation a data value is from the mean, the further away from the mean it is. 6.3 Standard Deviation and z-Scores 1 To get the z-score, we get the data value and subtract it by the mean, then we divide by the standard deviation. Population z = x−μ σ Sample z-score z = x−xˉ s 6.3 Standard Deviation and z-Scores 2