Measures of Spread: Quartiles

The mean, as a single value, is a useful measure for describing the center of a distribution and where the most of the scores in the distribution are located. It does not tell us very much, however, about scores away from the center of the distribution and/or scores that occur infrequently.

To describe a data set accurately, we need to know not only where scores are centered but also about how much individual scores within the distribution differ from one another. Measures of variability provide context (consistency) for measures of center.

The statistical model for abnormality requires two statistical concepts:

a measure of the average and
a measure of the deviation from the average.

The fact that scores deviate from average means that they are variable. The goal is to measure the amount of variability for a particular set of scores.

Are scores clustered together, or are they scattered over a wide range of values?

A good measure of variability should:

provide an accurate picture of the spread of the distribution, and
give an indication of how well an individual score (or group of scores) represents the entire distribution.