How to use the Interquartile Range Calculator
Paste your numbers separated by commas, spaces or new lines. You get the first quartile, the third quartile and the interquartile range between them.
What the IQR tells you
The interquartile range is the spread of the middle half of your data. Because it ignores the lowest and highest quarter, a single extreme value cannot blow it up the way it does with the full range. That makes it a good measure of spread for skewed data like house prices or salaries.
Finding outliers
A common rule flags any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR as a possible outlier. If Q1 is 20 and Q3 is 30, the IQR is 10, so values under 5 or over 45 deserve a second look. Box plots draw their whiskers using exactly this rule.
The formula
IQR = Q3 − Q1. Outlier fences: Q1 − 1.5 × IQR and Q3 + 1.5 × IQR
Examples
- 2, 4, 6, 8, 10
IQR: 4
- 12, 15, 21, 22, 30, 34, 41, 55
IQR: 16.25
- With an outlier 10, 12, 13, 15, 16, 90
IQR: 3.5
Limitations and assumptions
Quartile methods vary slightly between textbooks and spreadsheets, so Q1 and Q3 can differ a little from other tools on small data sets.
Frequently asked questions
What is the IQR?
Q3 minus Q1.
How do I spot outliers with it?
Values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are usually flagged.
Why use IQR instead of range?
It ignores extreme values, so one outlier does not distort it.
Do quartile methods differ?
Slightly, so other software can give a slightly different answer.