Range

Descriptive Statistics and Describing the Characteristics of a Distribution Averages are only half of the story The other half is measures of variability

Variability Reflects how scores differ from one another 7, 6, 3, 3, 1 7, 6, 3, 3, 1 3, 4, 4, 5, 4 4, 4, 4, 4, 4 What is the average? X=4 Some Variability What is the average? X=4 Less Variability What is the average? X=4 No Variability

Variability (cont.) Can also be called spread or dispersion The smaller the dispersion (or variability), the more reliable the mean If the variability is small The mean is considered quite representative of the data The mean is a reliable average Conversely, if there is a large variability, the mean is not very reliable

Variability (cont.) Can be thought of as a measure of how different scores are from one another Think of it as “How different scores are from one particular score”

Variability (cont.) What score are we talking about? The mean. Variability becomes a measure of how much each score in a group of scores differs from the mean

Variability (cont.) The average is a representative score in a set of scores Now think about variability Variability reflects how different scores are from one another Together the average and the variability can describe the characteristics of a distribution and show how distributions differ from one antoher

Variability (cont.) Three measures of variability reflect the degree of variability, spread, or dispersion in a group of scores: Range Standard deviation Variance

Range Most general measure of variability Gives you an idea of how far apart scores are from one another Computed by subtracting the lowest score from the highest score r = h – l r = range h= highest score l=lowest score

Range (cont.) Is used to get a very general estimate of how wide or different scores are from one another How much spread there is from the lowest to the highest point in a distribution Should not be used to reach any conclusions regarding how individual scores differ from one another.