Range Calculator
How wide the data runs — max minus min, with the honest companions: midrange, the Moore-McCabe IQR, and Tukey fences that flag the outliers by rule instead of by vibe.
Range Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Univariate only — one list per run
- Quartile convention fixed (exclusive); no interpolated types
In short: The range of 12, 15, 18, 22, 28 is 28 − 12 = 16. The midrange is (12 + 28)/2 = 20. By the exclusive Moore-McCabe convention Q1 = 13.5, Q3 = 25, so IQR = 11.5 and the Tukey fences sit at 13.5 − 1.5 × 11.5 = −3.75 and 25 + 1.5 × 11.5 = 42.25 — no value strays outside. On 3, 7, 9, 15, 100 the range is 97 but the IQR is 52.5 and even 100 stays inside the fence.
Formula
range = max − min
IQR = Q3 − Q1 (Moore-McCabe)
fences: Q1 − 1.5·IQR / Q3 + 1.5·IQR
the range reads the tails; the IQR reads the crowd.
Worked Example
- Sort. the minimum and maximum are endpoints of the sorted line — everything on this page is positional.
- Subtract. range = max − min: the whole width, tails and all.
- Halve the question. IQR = Q3 − Q1 is the width of the middle 50% — the same data measured where it crowds.
One new maximum moves the range the whole way. The IQR does not move at all unless the MIDDLE of the data moves — that asymmetry is the entire point of computing both.
Strengths & Limits Of This Model
Where this engine is strong
- Range and IQR printed side by side with the convention named
- Fences computed and outliers flagged by rule
Where it stops
- No standard deviation on this page
- Exclusive quartiles differ from Excel’s inclusive on small n
Practical Use Cases
Delivery times
best case minus worst, and the normal band
Manufacturing tolerances
the fence that flags a rogue part
Budget variance
width of spend, robust to one wild invoice
Methodology & Editorial Standards
Sort the parsed values. Range = max − min. Midrange = (min + max)/2. Quartiles by the Moore-McCabe exclusive method: Q2 = median; for odd n the median is excluded from both halves; Q1 and Q3 are the medians of the halves; IQR = Q3 − Q1; Tukey fences at Q1 − 1.5·IQR and Q3 + 1.5·IQR with any value outside listed.
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.
Range Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
What is the range?
The distance from the smallest value to the largest: max − min. It is the simplest possible spread measure and the most fragile — it reads exactly two values and the other n−2 could be anything.
Why does the page also compute the IQR?
Because the range answers to the tails while most questions live in the middle. The interquartile range is the width of the middle 50% — Q3 − Q1 — and one extreme value cannot move it unless the crowd moves. Quoting both is how you tell a wide crowd from a narrow crowd with one outlier.
Whose quartile convention is this?
Moore and McCabe’s exclusive method — the same split as the TI-83/85: the median is found, then EXCLUDED from both halves when the count is odd, and Q1/Q3 are the medians of those halves. Other conventions (Tukey’s inclusive hinges, interpolation types) can give different quartiles on small sets — pick one, name it, keep it. This page names its convention on every card.
What are the Tukey fences?
An outlier RULE, not a vibe: flag anything below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. John Tukey chose 1.5 so that a clean symmetric sample flags nothing and a genuine tail flags loudly. This page prints the fences and lists anything outside them.
On 3, 7, 9, 15, 100 — is 100 an outlier?
Not by the fence. Q1 = 5, Q3 = 57.5, IQR = 52.5, upper fence = 57.5 + 78.75 = 136.25, and 100 is inside it. It IS the whole reason the range is 97 — an extreme that moves the tails without leaving the crowd. That distinction is exactly why the page computes both widths.
What is the midrange, and why the warning?
The midpoint of the endpoints, (min + max)/2 — the centre of the RANGE. It inherits the range’s fragility doubling down: one value can drag it anywhere, so it is quoted in physics and signal work but rarely in statistics. The median page computes the centre that resists.
Range page or Median page?
Different questions: how WIDE versus where is the MIDDLE. The median is a position and cannot see width at all; the range is a width and cannot see position. This page borrows the median once — to split halves for the quartiles — and the borrow is named.
Can the range be zero?
Only when every value is identical — 5, 5, 5, 5 has range 0, IQR 0, and fences of width zero at 5. That is not a refusal; it is a real (if boring) answer: the data has no spread worth measuring.