Five-Number Summary Calculator
The five-number summary is a foundational tool in statistics that provides a complete snapshot of your data in just five values: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. This calculator computes all five values, along with the range and interquartile range (IQR), giving you everything you need to understand your data's distribution. The five-number summary is the basis of box plots, a common visualization used in exploratory data analysis, and it works for any dataset regardless of shape or distribution.
Five-number summary definitions
Minimum = smallest value
Q1 = 25th percentile
Median (Q2) = 50th percentile
Q3 = 75th percentile
Maximum = largest value
Range = Maximum - Minimum
IQR = Q3 - Q1
The five numbers explained
- Minimum: The smallest value in the dataset. Sensitive to outliers.
- Q1: The 25th percentile. 25% of data falls below this value.
- Median: The 50th percentile or middle value. Divides data in half.
- Q3: The 75th percentile. 75% of data falls below this value.
- Maximum: The largest value in the dataset. Sensitive to outliers.
- Range: Total spread from minimum to maximum.
- IQR: Spread of the middle 50% of data, robust to outliers.
Five-number summary: frequently asked questions
What is a five-number summary?
A five-number summary consists of five values that describe your dataset: the minimum, Q1 (25th percentile), median (Q2, 50th percentile), Q3 (75th percentile), and maximum. These five values provide a quick overview of the distribution and spread of your data.
Why is the five-number summary useful?
The five-number summary gives you a complete picture of your data's spread and distribution using just five numbers. It is the basis for box plots and provides a simple, robust way to compare datasets without assuming any particular distribution shape.
What is the range?
The range is the difference between the maximum and minimum values: Range = Max - Min. It tells you the total spread of your data but is sensitive to outliers.
What is IQR and why is it included?
IQR (interquartile range) = Q3 - Q1. It represents the spread of the middle 50% of your data and is more robust than the range because it ignores extreme values.
How are the values ordered in the five-number summary?
The five values are always presented in order from smallest to largest: minimum, Q1, median, Q3, maximum. These divide the sorted data into four equal (or near-equal) sections.
Official sources
- NIST/SEMATECH e-Handbook of Statistical Methods: NIST Handbook.
- American Statistical Association: ASA.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.