1. 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: 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).

2. 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).