Five Number Summary Calculator
Enter a data set to instantly calculate its five number summary — minimum, first quartile (Q1), median, third quartile (Q3), and maximum — the same five values used to construct a box plot.
How the Five Number Summary formula works
The five values that summarize a data set's distribution:
Minimum = smallest value Q1 = median of the lower half Median = middle value of the full sorted data Q3 = median of the upper half Maximum = largest value
Step-by-step calculation
- Sort the data from smallest to largest.
- Identify the minimum and maximum values.
- Find the median of the full data set.
- Find Q1 (median of the lower half) and Q3 (median of the upper half).
Worked example
Data set: 3, 7, 8, 12, 13, 14, 18, 21, 25. Minimum = 3, Q1 = 8, Median = 13, Q3 = 21, Maximum = 25.
Frequently asked questions
What is this used for?
The five number summary is the standard basis for constructing a box plot (box-and-whisker diagram), and it gives a quick sense of a data set's center, spread, and range without needing every individual value.
How is this different from the Interquartile Range Calculator?
The Interquartile Range Calculator focuses specifically on Q1, Q3, and the IQR (Q3−Q1). This calculator gives the fuller five-value picture, adding the minimum, median, and maximum for more context.