IQR Calculator
The spread of the middle half: IQR = Q3 − Q1 on the site’s stated convention, with the robustness card that shocks the list’s maximum live — watch the SD jump while the IQR holds, and know why fences are built from quartiles.
IQR Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- One convention, stated — no three-way comparison (the quartile page owns that)
- IQR = 0 on piled-up middles is printed with its warning, not treated as an error
In short: The quartile page’s own list — 6, 7, 15, 36, 39, 40, 41, 42, 47, 49 — gives Q1 = 20.25 and Q3 = 41.75 under the interpolation convention, so IQR = 21.5: half the data live in a band 21.5 wide. The robustness card is the finding: bump the largest value 49 → 149 and the SD leaps 16.376134 → 40.515566 (2.474062×) while the IQR does not move — spread measured by quartiles is measured by positions, not by every point. The fences preview (−12, 74) hands the flagging question to the outlier page; the convention card states plainly that another convention (Tukey’s halves) would quote 27 on this same list.
Formula
IQR = Q3 − Q1 · fences = Q1 − 1.5·IQR, Q3 + 1.5·IQR
The quartiles use the interpolation convention (the percentile page’s), stated rather than silent — the quartile page shows all three conventions side by side on the same list.
Worked Example
- Paste 4 to 500 values (the default is the quartile page’s own list).
- Read Q1, Q3 and the IQR — the band holding the middle half.
- Read the robustness card: your list with its maximum shocked, SD vs IQR.
- Follow the fences preview to the outlier page for the flagging question.
Defaults: Q1 20.25, Q3 41.75, IQR 21.5; robustness bump 49 → 149 moves SD 16.376134 → 40.515566 (×2.474062) with the IQR unmoved; fences preview (−12, 74).
Strengths & Limits Of This Model
Where this engine is strong
- Robustness priced live on your own list — the SD-vs-IQR shock, computed
- Convention stated on the card so the number can be reconciled with other tools
Where it stops
- No weighted or trimmed variants
- Does not flag anything itself — the fences preview hands off
Practical Use Cases
Reporting
spread that survives its own outliers
QC
the band where the middle half lives
Teaching
breakdown points: 25% vs 0%
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.
IQR Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why quote IQR instead of SD?
Because of what each tolerates. The SD squares every deviation, so one wild value can own it — the robustness card shocks your max and the SD jumps 2.474062× while the IQR holds 21.5. The IQR’s breakdown point is 25%: nearly a quarter of the data could be garbage before the middle-half band lies. The SD’s is 0%.
Why 21.5 here and 27 on the quartile page’s Tukey row?
Conventions. This page uses the interpolation convention (the percentile page’s): Q1 = 20.25, Q3 = 41.75, IQR = 21.5. The halves methods — Tukey’s and Moore–McCabe’s — put the quartiles at 15 and 42, IQR 27, on this same list. The convention card states the choice; the quartile page shows all three side by side.
What exactly does “the middle half” mean?
Sort the list: a quarter of the values sit below Q1, a quarter above Q3, and the IQR is the width of what remains — the band the typical member lives in. It is spread with the top and bottom quarters amputated, which is precisely why it survives amputation-worthy data.
Where do the fences come in?
The preview card builds the outlier gates from YOUR IQR: Q1 − 1.5·IQR and Q3 + 1.5·IQR — (−12, 74) on the defaults. Actually flagging points, naming positions and grading severity is the outlier page’s question; the two pages share the convention so the hand-off is seamless.
Can the IQR be zero on non-constant data?
Yes — if more than half the values are identical, the middle half can be a single point and the IQR collapses to 0 while the tails still move. The page prints it with that warning: a zero-width middle is information about the pile-up, not proof of a constant process.
Why does the robustness card shock the MAXIMUM?
Because the max is where an outlier attacks first. Doubling the story: the card computes your list’s SD, recomputes with the largest value replaced by largest + 100, and shows both spreads — SD 16.376134 → 40.515566, IQR unchanged. The gap between those two reactions is the entire argument for resistant statistics.
Is IQR the same as the range’s middle?
No — the range is max − min (every point counts, 0% robust); the IQR is Q3 − Q1 (only positions count). On the defaults the range is 43 and the IQR 21.5 — the range answers “how wide is everything”, the IQR “how wide is the crowd”.
Why does this page exist beside the quartile page?
Different questions on the same quartiles: the quartile page owns the POSITIONS — three named conventions side by side on the same list — while this page owns the SPREAD verdict built from one stated convention, plus the robustness shock the positions alone cannot show. Same arithmetic underneath; the hand-offs run both ways.