Chapter 3 Variability Variability – how scores differ from one another. Which set of scores has greater variability? Set 1: 8,9,5,2,1,3,1,9 Set 2: 3,4,3,5,4,6,2,3 Means are Set 1: 4.75 and Set 2: 3.75. Tells us nothing of variability. Variability is more precisely how different scores are from the mean. Computing the Range Subtract the lowest score from the highest (r=h-l) What is the range of these scores? 98,86,77,56,48 Answer: 50 (98-48=50) Computing the Standard Deviation The standard deviation (s) is the average amount of variability in a set of scores (average distance from mean).

Formula: Compute s for the following: 5,8,5,4,6,7,8,8,3,6 So, an s of 1.76 tells us that each score differs from the mean by an average of 1.76 points. *Why n-1? N represents the true population and n-1 represents the sample. Since we are projecting onto the sample, it is better to overestimate the variability (be conservative). The larger the sample size, however, the less of a difference this will make. Purpose: to compare scores between different distributions, even when the means and standard deviations are different (e.g., men and women). Larger the s the greater the variability. Computing Variance – simply s2 (really only used to compute other formulas and techniques). Difference: Variance is stated in units that are squared (not original units).