Range & Interquartile Range Calculator
Enter a list of numbers to get the minimum, maximum, range, quartiles Q1 and Q3, and the interquartile range (IQR) with outlier fences.
How it works
Range = max − min · IQR = Q3 − Q1 · quartiles by linear interpolation · outlier fences = Q1 − 1.5·IQR and Q3 + 1.5·IQR
The range is the simplest measure of spread — the distance from the smallest to the largest value — but a single extreme point can blow it up. The interquartile range is the range of the middle half of the data (Q3 minus Q1), so it ignores the tails and is far more robust to outliers. The classic 1.5 × IQR fences flag values that sit unusually far from the central box, the same rule that draws the whiskers on a box plot.
Worked example
For 10, 12, 14, 15, 18, 19, 20, 22, 25, 30 the minimum is 10 and maximum 30, a range of 20. Q1 ≈ 14.25 and Q3 ≈ 21.5, so the IQR is about 7.25. The fences fall at roughly 3.4 and 32.4, so none of the values are flagged as outliers.
Sources: Interquartile range — Wikipedia
Frequently asked questions
How are the quartiles calculated here?
Q1 and Q3 use linear interpolation on the sorted data (the same method as Excel’s PERCENTILE.INC and R’s type 7). Other conventions exist and can give slightly different quartiles for small samples, so results may differ from a textbook that uses a different rule.
Why prefer the IQR over the range?
The range depends entirely on the two most extreme values, so one outlier can dominate it. The IQR measures the spread of the central 50% of the data and is unaffected by extreme points, making it a more stable description of typical spread.
What counts as an outlier?
By the common Tukey rule, a value is a potential outlier if it lies more than 1.5 × IQR below Q1 or above Q3. This calculator lists any such values, but "potential outlier" is a flag for inspection, not automatic grounds for removal.
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This calculator is for educational purposes. Double-check important results before acting on them.