Interquartile Range Calculator
Focusing on the Middle 50%, Not the Extremes
The interquartile range describes how spread out the core of a data set is by ignoring the top and bottom quarters entirely. It's the width of the box in a box-and-whisker plot, and it's the standard tool for flagging outliers — a value far outside the IQR is exactly what those "whiskers" on the plot are pointing at.
The Formula
Q1 (the first quartile) is the median of the lower half of the sorted data; Q3 (the third quartile) is the median of the upper half. This calculator uses the exclusive median method, where the overall median itself is excluded from both halves when the data set has an odd count.
Worked Example
| Sorted values | Q1 (lower half median) | Q3 (upper half median) | IQR |
|---|---|---|---|
| 7, 15, 36, 39, 40, 41 | 15 | 40 | 25 |
The Standard Outlier Rule
A widely used convention treats any value falling more than 1.5 × IQR below Q1 or above Q3 as an outlier worth investigating — this is exactly what determines whisker length on a standard box plot.
Where This Matters
- Outlier detection — the 1.5×IQR rule is the most common systematic method for flagging unusual data points.
- Box plots — the IQR literally defines the box in a box-and-whisker chart.
- Skewed data — because it's based on quartiles rather than the mean, IQR remains meaningful even when a distribution is heavily skewed.
- Income, pricing, and duration data — any measure with a long tail benefits from a spread statistic that isn't dominated by that tail.
How to Use This Calculator
- Enter at least four numbers into the values field, separated by commas.
- Select Calculate.
- The result shows the sorted data, Q1, Q3, and the resulting IQR.
Related Calculations
Use the Median Calculator to find the overall middle value, or the Range Calculator for a simpler (but outlier-sensitive) measure of total spread.