Now that we have determined ways to describe measures of central tendency for a data set we must determine measures of the extent to which individual values differ from the mean.

The most common measure of dispersion is the range.

For nominal variables, since the categories are not ordered, the range is simply the number of categories with at least one response. For other variables, the range is the difference between the highest and lowest value.

For ordinal, and quantitative variables there is another way to think about variation, which is a natural extension of concept of the median. The median is the measure of the 50th percentile, with 50% of the data falling below the median and 50% of the data falling above. The 0th and 100th percentile would be the range of data.

The data can also be divided into quartiles using cut points of 25 percent, 50 percent, and 75 percent. The Interquartile Range (IQR) is the difference between the 25th and 75th percentile. The IQR is essentially a measure of the middle 50 percent of the data, and therefore is not greatly affected by outliers and extreme data points.