Five-Number Summary from a List Calculator
Get the five-number summary of a data set — minimum, first quartile, median, third quartile and maximum — plus the range and IQR.
How it works
Sort the data · Min, Max = extremes · Q1, Median, Q3 = 25th, 50th, 75th percentiles (linear interpolation) · IQR = Q3 − Q1
The five-number summary describes a data set with five landmarks: the minimum, the first quartile (25% of the data lies below it), the median, the third quartile, and the maximum. Together they show centre, spread and skew at a glance and are exactly the values a box plot draws. This calculator computes the quartiles by linear interpolation on the sorted data — the method Excel’s PERCENTILE.INC and numpy use — so a quartile can land between two observations.
Worked example
For 4, 8, 15, 16, 23, 42 (already sorted, n = 6): min = 4, max = 42, and the median is the average of the 3rd and 4th values, (15 + 16) ÷ 2 = 15.5. Linear interpolation gives Q1 = 9.75 and Q3 = 21.25, so the IQR is 21.25 − 9.75 = 11.5 and the range is 42 − 4 = 38.
Sources: Five-number summary — Wikipedia
Frequently asked questions
Which quartile method does this use?
It uses linear interpolation between order statistics — the inclusive method behind Excel PERCENTILE.INC and numpy’s default. Other tools may use Tukey’s hinges and differ slightly on small samples.
What does the five-number summary tell me?
It captures the centre (median), the spread of the middle half (Q1 to Q3), and the overall extent (min to max), which together reveal skew and the presence of long tails.
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This calculator is for educational purposes. Double-check important results before acting on them.