The interquartile range, or IQR, can be found after the median has been determined by dividing the data sets that are above and below the median in half, which divides the entire set into quarters, and then combining the second quarter with the third quarter. The resulting range is the IQR and represents the middle 50 percent of the entire data range. This splits the data set into three ranges, or quartiles: the first quartile (Q1) is the 25 percent of the data range below the IQR, the third quartile (Q3) is the 25 percent of the data range above the IQR and the IQR can be described as Q3 subtracted from Q1.
The IQR is also called the "middle fifty" or the "midspread" and is used to measure statistical dispersion in descriptive statistics. When a box plot is made of the data, the three quartiles can be easily seen as a graphical representation of a probability distribution. A useful application of the interquartile range is to determine the outliers in data.
Descriptive statistics, in which the IQR plays an important role, involves the organizing and summarizing of data so that it can be more easily understood. Unlike inferential statistics, the objective of descriptive statistics is to describe data without attempting to make inferences from the sample being examined to the entire population.