Q1 is the median of the lower half, Q3 the median of the upper half. IQR = Q3 − Q1.
Calculation details
Planning estimate only, not financial, tax, or legal advice. Verify assumptions and current rules before making decisions.
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Use this result
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What does this calculator estimate?
For the data 1, 3, 5, 7, 9, 11, the median (Q2) is the mean of 5 and 7 = 6. The lower half 1, 3, 5 gives Q1 = 3; the upper half 7, 9, 11 gives Q3 = 9; the interquartile range is 9 - 3 = 6.
- Quartiles split sorted data into four equal parts; the IQR is Q3 - Q1.
- The interquartile range is a robust spread measure less sensitive to outliers than the range.
- The IQR is often used to flag outliers with the 1.5 x IQR rule.
What quartiles measure
Quartiles split ranked data into four equal groups, showing where the middle of the data sits and how spread out it is. The IQR describes the spread of the central 50%, which is robust to extreme outliers.
Limitations to watch for
There are several quartile conventions (inclusive vs exclusive medians); this tool uses the standard median-of-halves method. Quartiles describe position, not magnitude — a huge gap between Q1 and Q3 isn't visible from the quartiles alone. Small data sets make quartile estimates unstable.
How to use it in practice
Use the five-number summary (min, Q1, median, Q3, max) to describe a distribution quickly. Use Tukey's fences to flag outliers: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR. Pair quartiles with a box plot for a visual.
['Enter at least two numbers.', 'The tool sorts and computes Q1, Q2, Q3, and IQR.', 'Values beyond the 1.5×IQR fences are flagged as outlier candidates.']
What quartiles are
Quartiles split a sorted dataset into four equal parts: Q1 is the 25th percentile, Q2 the median, Q3 the 75th. The interquartile range (IQR = Q3 − Q1) measures the middle spread. The calculator returns all of them from a dataset.
Why quartiles matter
Quartiles resist outliers better than the mean and range: a dataset with one huge value barely moves Q1/Q3. Box plots, salary reports, and test score distributions all use quartiles. The IQR is also the basis of the outlier rule (1.5 × IQR).
A worked example
[1, 2, 3, 4, 5, 6, 7, 8, 9]: Q1 = 3, Q2 = 5, Q3 = 7, IQR = 4. The calculator returns the full summary from a paste.
Computation conventions
Quartile methods differ slightly (inclusive vs. exclusive median splits); the calculator uses the common method and reports the numbers consistently.
Outlier detection
The 1.5 × IQR rule flags values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR as outliers. The calculator's quartiles feed the rule directly.
How this calculator works
Formula
Quartiles split the sorted data into four parts. Q2 is the median. Q1 is the median of the lower half (excluding the median when n is odd) and Q3 the median of the upper half. IQR = Q3 − Q1. Outlier fences: Q1 − 1.5×IQR and Q3 + 1.5×IQR.
Worked example
For [1, 3, 5, 7, 9, 11, 13, 15]: Q2 = (7 + 9) ÷ 2 = 8, Q1 = (3 + 5) ÷ 2 = 4, Q3 = (11 + 13) ÷ 2 = 12, so IQR = 12 − 4 = 8.
Assumptions to verify
- The median-of-halves (standard) quartile convention is used.
- The data is at least ordinal (sortable).
- Tukey fences are a heuristic for outliers, not a hard rule.
Frequently asked questions
What are quartiles?
Values that split sorted data into four equal parts: Q1 (25th percentile), Q2 (median), and Q3 (75th percentile).
How are quartiles calculated?
Find the median (Q2). Then find the median of the lower half for Q1 and the median of the upper half for Q3. IQR = Q3 − Q1.
What is the interquartile range (IQR)?
The spread of the middle 50% of the data (Q3 − Q1). It's robust to outliers, unlike the range.
How are outliers identified?
Tukey's fences: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are flagged as outlier candidates.
Why do quartile values differ between tools?
Different conventions exist for dividing the halves (some include the median in both halves). This tool uses the standard median-of-halves method.
What is a box plot?
A chart showing min, Q1, median, Q3, and max — the five-number summary — with whiskers and outlier points. Quartiles are its backbone.
Do quartiles work for any data set?
They work for ordinal or numeric data of at least 2 values. Very small sets produce unstable quartiles.
What is the IQR?
Q3 − Q1 — the middle 50% spread, robust to outliers.
How do I find outliers?
Below Q1 − 1.5×IQR or above Q3 + 1.5×IQR.
Why use quartiles?
They describe spread without being distorted by extreme values.
Cite this tool
BoringToolsKit. “Quartile Calculator.” boringtoolskit.com/quartile-calculator/ (reviewed 2026-08-25). Free to reference in articles, syllabi, and answer posts with a link.
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