interquartile

Interquartile is a statistical term commonly used in reference to the interquartile range (IQR), a measure of spread for the central portion of a data set. In a sorted data set, the values are divided into four equal parts by the quartiles. The first quartile (Q1) marks the 25th percentile, the second quartile (Q2) is the median, and the third quartile (Q3) marks the 75th percentile. The interquartile range is the difference between Q3 and Q1 and describes the dispersion of the middle 50 percent of the data.

Calculation and conventions vary slightly. To compute Q1 and Q3, the data are ordered and a quartile method is chosen; the resulting Q1 and Q3 determine the IQR as Q3 minus Q1. Different software packages may yield small variations in quartile values, especially for small samples, due to distinct calculation rules.

Interpretation and uses. The IQR provides a robust summary of variability because it focuses on the central portion of the distribution and is less affected by extreme values than the overall range. It is a standard component of descriptive statistics, and boxes in box plots typically extend from Q1 to Q3 with a median line at Q2. Outliers are often identified using the 1.5 times the IQR rule: values below Q1 minus 1.5 times IQR or above Q3 plus 1.5 times IQR.

Limitations. The IQR does not convey information about the shape of the distribution, skewness, or tails beyond the central 50 percent. It also depends on the quartile calculation method and on sample size, which can affect stability in small samples. In population contexts, interquartile measures are defined analogously to the sample case.