Find Q1, Q3, and the interquartile range of your data set instantly, with a full step-by-step solution.
The interquartile range (IQR) measures the spread of the middle 50% of your data. Unlike the range (max minus min), it isn't affected by extreme outliers, which makes it a more robust way to describe variability — especially alongside the median.
The IQR is the difference between the third quartile (Q3) and the first quartile (Q1) of a data set. Q1 is the value below which 25% of the data falls, and Q3 is the value below which 75% of the data falls. The IQR therefore captures the middle 50% of your data, excluding the lowest and highest quarters.
IQR = Q3 − Q1The IQR is commonly used to flag outliers with the "1.5 × IQR rule": any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is considered a potential outlier. This is the same rule used to draw the whiskers on a box plot.
Khan Academy's lesson on interquartile range walks through more worked examples of finding quartiles.
The range (max minus min) is heavily influenced by a single extreme value. The IQR only looks at the middle 50% of the data, so it gives a more stable picture of spread when your data has outliers.
The common rule is that any value below Q1 − 1.5×IQR, or above Q3 + 1.5×IQR, is flagged as a potential outlier. This same rule defines the whiskers on a box plot.
Yes. There are several accepted conventions for calculating quartiles (inclusive, exclusive, and interpolation-based methods), and they can give slightly different results, especially for small data sets. This calculator uses the exclusive method, which is common in introductory statistics courses.
A small IQR means the middle 50% of your data is tightly clustered. A large IQR means the middle half of your data is more spread out. Comparing IQRs is a common way to compare the spread of two data sets.