IQR stands for "interquartile range," a measurement of the location of the bulk of values in a set of data. The formula for finding the interquartile range is to subtract the first quartile from the third quartile.
The IQR can also be defined as the difference between the lower quartile and the upper quartile. When a set of data is divided into four equal parts, each part is called a quartile. IQR can also be described as the middle 50 percent of the data set. The smallest and largest data points in a set define the boundaries of the data set. The middle 50 percent is found within these boundaries.
The interquartile range is used to measure how spread out the data are from the mean in a given set. A lower IQR means the data points are closer together while a higher IQR means the data points are further apart. When IQR is used with measurements such as the median and total range, a more in-depth analysis can be made regarding a data set's tendency to cluster around the mean.
The term "interquartile range" was first introduced in 1879 by Sir Donald MacAlister when he used the terms "lower quartile" and "higher quartile." Francis Galton defined the term "interquartile range" in 1882.