Measures of Dispersion

1. Measures of Dispersion • as with averages, researchers need to transform data into a form conducive to interpretation, comparisons, and statistical analysis • measures of dispersion summarize differences in the data, how the numbers differ from one another.

2. Three Common Measuresof Dispersion • range • variance • standard deviation

3. range • the simplest measure of dispersion • represents the distance between the highest and lowest scores • sensitive to extreme scores • insensitive to differences between scores within a distribution Golf Scores 102 97 89 78 77 76 68 range = 34

4. variance • indicates the amount of variation or variability in a distribution • defined as “the average of the sum of the squared deviations” • “good” variance (between group) versus “bad” variance (within group)

5. standard deviation • the most sensitive measure of dispersion • the standard deviation reflects the average amount of dispersion in a distribution • defined as the square root of the variance • standard deviations and significance tests

6. standard deviations under the normal distribution