StatReason

Five-Number Summary Calculator

Enter a list of numbers to get the minimum, first quartile, median, third quartile, and maximum in one summary.

What this answers

The five-number summary answers "what does the overall shape and spread of this data look like, beyond just its average?" It is the same set of five values a box plot draws, giving you the raw numbers behind that picture: the two extremes, the middle value, and the two quartiles that mark off the middle half of your data.

How it is calculated

The minimum and maximum are simply the smallest and largest values. The median, first quartile (Q1), and third quartile (Q3) all use the Hyndman-Fan Type 7 interpolation method used consistently across this site, the same convention R and most spreadsheet software use by default, so these numbers will match what you get from those tools on the same data.

Worked example

For the values 1 through 5: the minimum is 1, Q1 is 2, the median is 3, Q3 is 4, and the maximum is 5, an evenly spaced summary reflecting the evenly spaced input data. Any real dataset with a skew or clustering will show that pattern in how unevenly these five points are spaced.

Assumption audit

Calculated from your data: all five summary values directly, using every value you entered, with no inference or estimation involved.
Evidence to review: how far apart Q1 and Q3 sit relative to the full min-to-max range. A middle-half range that is much narrower than the full range suggests extreme values worth a closer look with the Box Plot Maker.
You must verify: that all values are measured on the same scale, since combining incompatible units into one summary produces numbers with no coherent interpretation.

Common mistakes

Treating the five-number summary as a complete description of your data is a common oversight: it says nothing about the mean, and two datasets can share an identical five-number summary while looking completely different in the middle, since these five points ignore everything about how values are distributed within each quarter. Pairing this summary with the actual shape from a histogram avoids that blind spot.

Limitations

This summary does not report the mean or standard deviation, only order-based statistics. With very few values, quartiles can look arbitrary since there is little data to interpolate between, and a very small dataset may produce a five-number summary that overstates how precisely its center and spread are actually known.