Interquartile Range (IQR) Calculator

IQR = Q3 − Q1 — the middle 50% spread, robust to outliers.

Inputs

Result

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General calculation reads

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How Not to Be Wrong
Jordan Ellenberg - math thinking
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The Joy of X
Steven Strogatz - accessible math
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Scientific calculator (Casio fx-991EX)
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How to use this calculator

  • Enter your data.
  • Read IQR and Q1/Q3.
  • Inspect the outlier fence.

About this calculator

IQR — interquartile range — captures the middle 50% of the data. Robust to outliers because it ignores the top and bottom quarters. Often used with the Tukey 1.5×IQR rule to flag potential outliers.

Frequently asked

Why is IQR more robust than range or SD?+
IQR ignores the top and bottom 25% of the data, so a single extreme value can't pull it. SD weighs every value, so outliers move it a lot.
What is the 1.5 × IQR outlier rule?+
A datum below Q1 − 1.5·IQR or above Q3 + 1.5·IQR is flagged as a potential outlier. This is the Tukey convention used in box plots.
Is IQR always positive?+
Yes — Q3 ≥ Q1 by definition.
Can I use IQR for skewed data?+
Yes — IQR is great for skewed data because it's a quantile-based measure that doesn't assume symmetry.
How does IQR relate to box plots?+
The "box" is from Q1 to Q3; whiskers extend to the outlier fence; outliers are plotted as dots.

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