Chapter 3 Variability I Variability how scores differ

Chapter 3 Variability I. 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. II. 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) III. Computing the Standard Deviation The standard deviation (s) is the average amount of variability in a set of scores (average distance from mean).

A. 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. B. 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. IV. Computing Variance – simply s 2 (really only used to compute other formulas and techniques). Difference: Variance is stated in units that are squared (not original units).