Five number summary and box plot

Maths: Statistics for machine learning

2 min read

Published Oct 22 2025, updated Oct 23 2025

Machine LearningMathsNumPyPandasPythonStatistics

The Five-Number Summary gives a quick overview of how data is spread.
It consists of five key descriptive statistics that summarise the distribution of a dataset. It is made up from five numbers that we have already covered in the previous sections.

The Five Values:

Statistic	Meaning	Description
Minimum	The smallest value	The lowest observation in the data
Q1 (First Quartile)	25th percentile	25% of the data fall below this value
Median (Q2)	50th percentile	The middle value (half the data above, half below)
Q3 (Third Quartile)	75th percentile	75% of the data fall below this value
Maximum	The largest value	The highest observation in the data

Why It’s Useful

Gives a summary of data distribution (centre, spread, and extremes).
Helps identify outliers and skewness.
Foundation for creating a box plot — a key data visualisation tool.

The Box Plot

A Box Plot (or Box-and-Whisker Plot) is a graphical representation of the five-number summary.
It shows the spread, centre, and outliers of a dataset.

Parts of a Box Plot

The box spans from Q1 to Q3 (the interquartile range, IQR = Q3 - Q1).
The line inside the box shows the median (Q2).
The “whiskers” extend to the minimum and maximum values that are not outliers.
- Lower whisker: Q1 - (IQR * 1.5)
- Upper whisker: Q3 + (IQR * 1.5)
Outliers (if any) are plotted as individual points beyond the whiskers.