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Quartile Calculator

Split a data set into quartiles — minimum, Q1, median, Q3 and maximum — with the interquartile range, using linear interpolation.

Data values

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How it works

Q1 = 25th, Q2 = 50th (median), Q3 = 75th percentile by linear interpolation · IQR = Q3 − Q1

Quartiles divide sorted data into four equal parts: Q1 marks the 25th percentile, Q2 the median at the 50th, and Q3 the 75th, with the minimum and maximum bracketing the ends. Together they form the five-number summary that a box plot draws, and the gap between Q1 and Q3 — the interquartile range — captures the spread of the middle half. This calculator locates the quartiles by linear interpolation on rank p·(n − 1), the inclusive method used by most spreadsheets.

Worked example

For 1, 2, 3, 4, 5, 6, 7, 8, 9 the minimum is 1 and the maximum is 9. The median Q2 is 5, and interpolation places Q1 at 3 and Q3 at 7, so the interquartile range is 7 − 3 = 4. A quarter of the data lies in each of the four intervals the quartiles create.

Sources: Quartile — Wikipedia

Frequently asked questions

What is the difference between quartiles and percentiles?

Quartiles are just three specific percentiles — the 25th, 50th and 75th — that carve the data into four equal groups. Percentiles are the general idea of splitting data into 100 parts, so every quartile is a percentile but only three percentiles are quartiles.

Why might my quartiles differ from another calculator?

Several accepted methods exist for locating quartiles. This tool uses linear interpolation on rank p·(n − 1) — matching Excel’s PERCENTILE.INC and NumPy — so 1…9 gives Q1 = 3 and Q3 = 7; Tukey’s exclusive median method can return slightly different Q1 and Q3.

What does the interquartile range tell me?

The IQR is the width of the middle 50% of the data, from Q1 to Q3. Because it discards the top and bottom quarters, it measures spread while ignoring extremes, which makes it a robust companion to the median and the basis of outlier fences.

Related calculators

Interquartile Range (IQR) Calculator

Find the interquartile range of a data set — the spread of the middle 50% — with Q1, Q3, the median and the 1.5×IQR outlier fences.

Five-Number Summary Calculator

Get the five-number summary — minimum, Q1, median, Q3 and maximum — plus the interquartile range and outlier fences for any data set.

Percentile Calculator

Find the percentile rank of a value in a data set, or the value at any percentile, with the Excel, nearest-rank and (n + 1) methods side by side, a full percentile table, quartiles and the worked steps.

Outlier Calculator

Detect outliers in a data set using Tukey’s 1.5×IQR rule — see which values fall outside the fences, plus the quartiles and fence bounds.

Mean Median Mode Calculator

Paste a list of numbers and get the mean, median, mode, range, sum and count at once.

For education — check assumptions (sample size, distribution) before using statistics in real decisions.