How this calculator works
The five values describe the ends and centre of an ordered data set. Linear interpolation uses position 1 + (n - 1)p. Medians of halves exclude the middle observation when n is odd; nearest rank selects an observed value. The minimum and maximum include all observations, even potential outliers. A single observation supplies all five numbers.
Formula
Summary = minimum, Q(0.25), median, Q(0.75), maximum; IQR = Q3 - Q1.
Worked example
For 5, 1, 4, 2, 3, linear interpolation gives 1, 2, 3, 4, 5. The interquartile range is 4 - 2 = 2.
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Frequently asked questions
Why do quartile answers differ?
Several accepted algorithms place quartiles differently in a finite sample. State the convention alongside the result.
Is the maximum the upper box-plot whisker?
Not always. A fenced box plot may end its whisker at the last non-outlying observation.
Can I mix measurement units?
Convert observations to one unit first. The five summary values then use that same unit.