What this calculator does
The interquartile range, or IQR, is the spread of the middle half of a data set: the distance between the point a quarter of the way up the sorted list, Q1, and the point three-quarters of the way up, Q3. Because it ignores the top and bottom quarters entirely, it describes typical spread without letting a handful of extreme values distort the picture the way the full range does.
This IQR calculator takes a list of numbers and returns Q1, Q3, the median and the interquartile range itself as the headline figure, using linear interpolation between the two data points either side of each quartile position. For the fuller set of descriptive statistics, including mean and standard deviation, or for the outlier cutoffs the IQR feeds into, those sit on their own dedicated pages.
The formula
Sort the data, then find Q1 and Q3 at the 25th and 75th percentile positions using linear interpolation: position i = (n − 1) × p for percentile p, then interpolate between the values at the floor and ceiling of that position. IQR is simply Q3 minus Q1, the width of the middle 50% of the sorted data.
| Term | Meaning |
|---|---|
| Q1 | The first quartile, the value below which the lowest 25% of the data falls. |
| Q3 | The third quartile, the value below which the lowest 75% of the data falls. |
| IQR | Interquartile range: Q3 − Q1, the spread of the middle half of the data. |
The inputs explained
| Field | What to enter |
|---|---|
| Data (comma or space separated) | A list of numbers separated by commas, spaces or line breaks. At least two values are needed, though quartiles are more meaningful with a longer list. |
When to use it
Describing spread when outliers are present
A data set with one or two extreme values makes the full range misleading, since it is entirely determined by whichever point sits furthest out. The IQR, built only from the middle half, is far less sensitive to that kind of distortion.
Comparing consistency across two data sets
Two groups can share a similar median while differing sharply in how tightly the middle 50% of their values cluster around it. Comparing IQR figures side by side captures that difference directly.
Setting up a box-and-whisker plot
A box plot is built around Q1, the median and Q3, with the box itself spanning the IQR. Working these three figures out first is the direct input needed before the whiskers and any outlier points are added.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How Q1, Q3 and IQR respond to one added high value
The same nine core values, 12, 15, 11, 18, 22, 15, 9, 14, 20, with a tenth value appended at increasing size.
| Added tenth value | Q1 (lower quartile, 25th percentile) | Q3 (upper quartile, 75th percentile) |
|---|---|---|
| 21 | 12.500 | 19.500 |
| 40 | 12.500 | 19.500 |
| 100 | 12.500 | 19.500 |
| 500 | 12.500 | 19.500 |
Questions
How do you find the IQR?
Sort the data, find Q1 (the 25th percentile) and Q3 (the 75th percentile), then subtract: IQR = Q3 − Q1. Several methods exist for pinpointing the exact quartile positions in a small data set; this calculator uses linear interpolation between neighbouring values.
How do you calculate IQR by hand for a small list?
Order the numbers from smallest to largest, split the list at the median into a lower and upper half, then find the median of each half: that gives Q1 and Q3. This simple method is close to, but not always identical to, the interpolation method used here, particularly for small data sets.
Why use the IQR instead of the range?
The range is just the maximum minus the minimum, so a single unusually high or low value sets it entirely. The IQR only looks at the middle 50% of the data, so a stray extreme value barely moves it, making it a more stable measure of typical spread.
What is a large or small IQR?
There is no fixed threshold; it depends entirely on the scale and nature of the data being measured. What matters is the comparison: a smaller IQR relative to a similar data set means the middle half of the values are packed more tightly together.
For mean, median, mode and standard deviation alongside the quartiles, see the descriptive statistics calculator. For the outlier cutoffs the IQR is used to set, see the outlier fences calculator.