What is the five number summary?

It is the set of five values that summarise a data set: the minimum, the first quartile, the median, the third quartile and the maximum. Together they describe the centre, spread and extremes of the data, and they are exactly the values used to draw a box plot.

How are the quartiles calculated?

The data is sorted and the quartiles are found as the 25th and 75th percentiles, using linear interpolation between the nearest values. This is the standard method used in most statistical software and spreadsheets, so the results here match what you would get in those tools.

What is the five number summary used for?

It gives a quick, robust snapshot of a data set and is the basis of the box plot, which displays it visually. It is ideal for comparing two or more groups at a glance and for spotting skew, since it is not distorted by a single extreme value.

Five Number Summary Calculator

This calculator finds the five number summary of a data set, the minimum, first quartile, median, third quartile and maximum, the five values that concisely describe a distribution and form the basis of a box plot. The five number summary is a staple of descriptive statistics because it captures the centre, the spread and the extremes of data in just five numbers, and it does so robustly, without being thrown off by the odd extreme value the way a mean and standard deviation can be. The minimum and maximum mark the range, the median marks the centre, and the two quartiles mark the boundaries of the middle half of the data. Together they tell you where the data sits, how spread out it is, and whether it leans to one side. They are exactly the values a box plot draws, with the box spanning the quartiles and whiskers reaching to the extremes. This tool computes them for you. You paste or type your numbers, and the calculator sorts them and returns all five values, plus the range and the interquartile range for good measure. The results update as you edit the data, so you can immediately see how a new value shifts the summary. Use it to summarise a data set, to prepare a box plot, to compare two groups at a glance, or for statistics homework. The quartiles use the standard interpolation method, consistent with most spreadsheets and software, so the results match what you would get elsewhere. The five number summary is often the quickest honest snapshot of a set of numbers.

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Your numbers (space, comma or line separated)

15.5

median (Q2)

Minimum4

Q19.75

Q321.25

Maximum42

Five number summary: min, Q1, median, Q3, max. Quartiles use linear interpolation. The range and IQR are shown in the note line as you compute.

How it works

The numbers are sorted in order. The minimum and maximum are the smallest and largest values. The median is the middle value, the 50th percentile. The first and third quartiles are the 25th and 75th percentiles, found by linear interpolation between the nearest data points, marking the boundaries of the middle half of the data.

Worked example

For 4, 8, 15, 16, 23, 42, the minimum is 4 and the maximum is 42. The median is the average of the two middle values, 15 and 16, which is 15.5. The first quartile is about 9.75 and the third quartile about 21.25, so the middle half of the data spans roughly 9.75 to 21.25.

Related calculators

Quartile & IQR: quartiles and spread.
Percentile Calculator: any percentile.
Mean Median Mode: averages and range.
Standard Deviation: variability.

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