Quartile Calculator
One list, three named conventions: Tukey’s inclusive hinges, Moore–McCabe’s exclusive medians-of-halves, and the Minitab/Excel interpolated quartiles — computed side by side so the disagreement is evidence, not error.
Quartile Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- 4 to 500 values; the three named conventions only (QUARTILE.EXC is a fourth the page does not ship)
- No outlier fences — they inherit whichever IQR you pick
In short: On 6, 7, 15, 36, 39, 40, 41, 42, 47, 49 the halves method gives Q1 = 15 and Q3 = 42 (IQR 27), while Excel’s interpolation gives Q1 = 20.25 and Q3 = 41.75 (IQR 21.5) — the same data, four positions apart at the first quartile, and neither is wrong. On odd-sized lists even the two halves methods split: 1 through 9 gives 2.5 and 7.5 under Moore–McCabe (median excluded from both halves) but 3 and 7 under Tukey’s hinges (median included in both). The convention is part of the answer, and this page prints all three with their reasoning — which is exactly the question the range page’s own limits hand off.
Formula
halves methods: split at the median, take each half’s median
interpolated: position 1 + p(n−1), p = 0.25 and 0.75
every textbook is describing the same three cutpoints — they disagree only about which values belong in each half and whether to round between values.
Worked Example
- Sort. every convention starts from the same ordered list; nothing below depends on input order.
- Halves twice. Tukey includes the median in both halves when n is odd; Moore–McCabe excludes it. Even n makes them identical.
- Interpolate. Excel/Minitab never split at all — they read the 25% and 75% positions straight off the list with linear interpolation.
6, 7, 15, 36, 39, 40, 41, 42, 47, 49: halves Q1 = 15, Q3 = 42; interpolated 20.25 and 41.75. On 1–9 the halves themselves split: exclusive 2.5/7.5, inclusive hinges 3/7.
Strengths & Limits Of This Model
Where this engine is strong
- All three conventions computed on the same list, never merged
- The exact positions where your list splits are named
Where it stops
- No QUARTILE.EXC mode
- No adjusted boxplot for skew
Practical Use Cases
Boxplot checks
software disagreed? now you know why
Textbook comparisons
both conventions quoted beside each other
Exam grading
name the convention your mark scheme uses
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Quartile Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why do quartile conventions disagree at all?
Because “the value 25% of the way in” has no single meaning for a finite list. Halves methods take medians of sub-lists and inherit the same even/odd question one level down; interpolation places the quantile continuously between values. Each convention is a defensible answer to an under-specified question, which is why this page never collapses them into one.
Which convention should I use?
The one your course, textbook or software specifies. Moore–McCabe is the classic statistics-classroom convention (and the range page’s fixed choice); Tukey’s hinges belong to boxplots as he drew them; Excel’s QUARTILE.INC and Minitab interpolate. When n is large the three converge — the disagreement is a small-sample phenomenon, which is why the page says exactly where your own list splits.
Why do the two halves methods agree on even n?
Because an even-sized list splits into two halves with no median value left over. The conventions differ only in where the median VALUE goes when it is an actual data point — into no half (exclusive) or both (inclusive). Even n: no leftover, no disagreement.
What is Excel’s QUARTILE.INC actually doing?
Reading position 1 + 0.25(n−1) along the sorted list and interpolating linearly between neighbours. On the ten-value default that is position 3.25 — a quarter of the way from the 3rd value (15) to the 4th (36), landing on 20.25. QUARTILE.EXC uses a different position law and disagrees yet again; this page ships the inclusive one and names it.
Why is one IQR bigger than the other?
Because the conventions place the cuts differently, not because the data changed. On the default list the halves IQR is 27 and the interpolated IQR is 21.5 — the interpolated cuts sit deeper inside the middle mass. Outlier fences built on the IQR inherit the difference, which is why two tools can flag different outliers on the same data.
Does the median itself ever disagree?
No — all three conventions compute the same median; the disagreement lives entirely in the quarter cuts. If a tool reports a different median for the same list, someone has an arithmetic bug rather than a convention.
Why not just pick one convention for me?
Because the choice belongs to your context and the page refuses to hide it. Printing one number would feel authoritative and quietly contradict your textbook half the time. Three labelled numbers with the disagreement explained is the honest product.
How big can the list be?
Five hundred values. With hundreds of points the three conventions typically land within a fraction of one position — the page still prints all three, because “typically” is not a guarantee it is willing to make silently.