Interquartile Range Calculator 2026
Instantly calculate IQR, Q1, Q2, Q3, outliers, and the full five-number summary from any dataset. Paste your numbers and get a complete statistical breakdown with a box plot.
Dataset Input
Enter your numbers separated by commas, spaces, or new lines
— values entered
Exclusive: Q1/Q3 from halves excluding the median. Inclusive: median is included in both halves when n is odd.
Statistical Results
IQR, quartiles, five-number summary, and outliers
Enter your dataset above and click Calculate IQR to get a full statistical breakdown.
How to Calculate IQR by Hand
Follow these five steps to find the interquartile range of any dataset, exactly as this calculator does it.
Interquartile Range FAQ
Everything you need to understand the IQR, from the basics of quartiles to outlier detection and choosing the right method.
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1): IQR = Q3 − Q1. It measures the spread of the middle 50% of a dataset and is a robust measure of statistical dispersion that is resistant to the influence of extreme values or outliers.
1) Sort the data in ascending order. 2) Find Q2 (the median) — the middle value, or the average of the two middle values for an even-count dataset. 3) Split the data into a lower half and upper half. 4) Q1 is the median of the lower half. 5) Q3 is the median of the upper half. 6) IQR = Q3 − Q1.
Use the 1.5 × IQR rule: any value below Q1 − 1.5×IQR (the lower fence) or above Q3 + 1.5×IQR (the upper fence) is flagged as a mild outlier. For extreme outliers, the threshold is 3 × IQR, giving a lower extreme fence of Q1 − 3×IQR and an upper extreme fence of Q3 + 3×IQR.
The five-number summary is a compact description of a dataset using five values: the minimum, Q1, Q2 (median), Q3, and the maximum. Together they describe where the data is centred, how spread out it is, and where the extremes lie. These five numbers are also what define a box-and-whisker plot.
When n (the count) is odd, the two methods treat the median differently. The exclusive method (Moore & McCabe) excludes the median when splitting data into lower and upper halves, which tends to give a wider IQR. The inclusive method (Tukey) includes the median in both halves, giving a narrower IQR. For even n, both methods produce the same result. Most statistics textbooks and exam boards use the exclusive method.
IQR is preferred when your data is skewed, has outliers, or does not follow a normal distribution, because it only considers the middle 50% of values and is therefore robust. Standard deviation is more appropriate for symmetric, normally distributed data where every value carries meaningful information. In exploratory data analysis, IQR is typically reported alongside the median rather than the mean.