    Chapter 4: Analysing the Data Part II : Descriptive Statistics # Variability

The average score in a distribution is important in many research contexts. So too is another set of statistics that quantify how variable (or "how dispersed") the scores tend to be. Do the scores vary a lot, or do they tend to be very similar or near each other in value? Sometimes variability in scores is the central issue in a research question. Variability is a quantitative concept, so none of this applies to distributions of qualitative data.

There are many intuitively appealing but little used measures of variability. The range, for example, is the difference between the largest and smallest score in the data set. The interquartile range or IQR is the difference between what we will later call the 25th and 75th percentile scores. By far the most widely used measures of variability are those to do with averaging how spread out the scores are from the mean. These are the Sums of Squares (SS), the standard deviation (s, or sd), and the variance (s2 or "var").

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