Last updated: March 2, 2026 by Dr. David Park

Five-Number Summary and Box Plots

Formula

Sort the data.
Min = smallest value.
Q1 = 25th percentile.
Median = 50th percentile.
Q3 = 75th percentile.
Max = largest value.

The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It provides a concise description of a dataset's distribution.

The five-number summary is the foundation of box plots (box-and-whisker diagrams), which visually display the spread, skewness, and potential outliers in data.

Common use cases:

  • Quick data distribution overview
  • Box plot construction
  • Comparing distributions across groups

Frequently Asked Questions

DD

Dr. David Park

Applied Mathematician, PhD Mathematics

David holds a PhD in Applied Mathematics from MIT. He has published research on numerical methods and computational algorithms used in engineering and scientific calculators.

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