How to use this five-number summary calculator
Paste your data above and press Calculate. You will receive the five numbers (minimum, Q1, median, Q3, maximum), the exact ingredients of a box plot, plus the IQR and range they imply.
What is the five-number summary?
Five numbers that sketch a whole distribution: where it starts (minimum), where its middle half lives (Q1 to Q3), where its centre sits (median), and where it ends (maximum). John Tukey designed the summary as the numerical twin of the box-and-whisker plot. If you can say the five numbers, you can draw the box, and vice versa.
Ten quiz scores: 58, 72, 65, 80, 91, 67, 72, 74, 69, 72 give a five-number summary of 58, 67.5, 72, 73.5, 91. Read left to right it tells the whole story: the floor (58), a typical lower score (67.5), the centre (72), a typical upper score (73.5), and the ceiling (91). The box of a box plot would run from 67.5 to 73.5 with a line at 72; narrow box, long whiskers: a consistent class with a couple of unusual results at the edges.
Reading the shape from the numbers
- Median close to the centre of Q1–Q3 means roughly symmetric data.
- Median hugging Q1 means the upper half is stretched: right-skewed data.
- A whisker (min–Q1 or Q3–max) much longer than the other points to outliers or a long tail on that side.
Comparing two groups' five numbers side by side (two classes, two treatments, two seasons) is one of the fastest honest comparisons in all of statistics.
Frequently asked questions
What are the five numbers in a five-number summary?
The minimum, first quartile (Q1), median, third quartile (Q3) and maximum of the dataset.
How does the five-number summary relate to a box plot?
The box runs from Q1 to Q3 with a line at the median, and the whiskers extend to the minimum and maximum (or to the furthest values inside the 1.5×IQR fences).
Does the five-number summary include the mean?
No, deliberately. It is built entirely from order statistics, so it holds up when outliers would distort the mean.