Interquartile Range Calculator
Paste your numbers to get Q1, Q3 and the interquartile range, with the outlier fences worked out for you.
- Both quartile methods
- Outliers flagged
- Shows the working
- Free
Find the interquartile range
Separate with spaces, commas or new lines. At least two numbers.
Only matters when you have an odd count. Textbooks differ, so pick the one your class uses. Spreadsheets and statistics packages often use a third, interpolating method that can give a slightly different answer again.
Show the working
How to find Q1, Q3 and the IQR
Sort and split
Put the numbers in order and find the median. That splits the list into a lower half and an upper half.
Median of each half
Q1 is the median of the lower half, Q3 the median of the upper half. With an odd count, decide whether the middle value joins a half.
Subtract
IQR = Q3 − Q1. It is the width of the middle 50% of the data, so one extreme reading barely moves it.
A value is usually called an outlier when it sits below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. Those two limits are the fences shown above. The 1.5 is a widely used convention, not a proof that the value is wrong, so treat a flagged reading as worth a second look.
Questions people ask
What is the interquartile range?
The width of the middle half of your data: Q3 minus Q1. It tells you how spread out the typical values are while ignoring the extremes at both ends.
How do I find Q1 and Q3 by hand?
Sort the numbers, find the median, then take the median of the lower half for Q1 and the median of the upper half for Q3.
Why do I get a different Q1 than my textbook?
Because there is more than one way to cut the data. The two methods taught in most classes both take the median of each half, and they disagree when the count is odd: the exclusive method (TI-84 calculators, Moore and McCabe) leaves the median out of both halves, while the inclusive method (Tukey’s hinges) keeps it in both. Use the dropdown to match your class. With an even count they agree. Spreadsheets and statistics packages usually interpolate between values instead, which can give a third answer that is not wrong either.
How does the IQR find outliers?
The usual rule draws a fence 1.5 × IQR below Q1 and 1.5 × IQR above Q3. Anything outside those fences is flagged as an outlier. It is a convention, not a law, so treat a flagged value as worth a second look rather than automatically wrong.
IQR or standard deviation?
Use the IQR when the data is skewed or has a few odd readings, because it ignores them. Use the standard deviation when the data is roughly symmetric and you want every value to count.
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