Quantile–Quantile (QQ) Plot

Maths: Statistics for machine learning

2 min read

Published Oct 22 2025, updated Oct 23 2025

Machine LearningMathsNumPyPandasPythonStatistics

A Quantile–Quantile (QQ) Plot is a visual tool used to compare the distribution of your data against a theoretical distribution (such as the Normal Distribution).
It plots the quantiles of your sample data against the quantiles of the reference distribution.

In simple terms:

“A QQ plot helps you see whether your data follow a straight line — if they do, it means your data come from the same distribution.”

How It Works

The x-axis represents the theoretical quantiles (from a known distribution, like Normal).
The y-axis represents the sample quantiles (from your data).
If the data follow the theoretical distribution, the points will lie close to a straight diagonal line (y = x).

Interpreting a QQ Plot

Pattern	Meaning
Points lie close to diagonal	Data follow the theoretical distribution
Points curve upward (above line at right tail)	Right-skewed (heavy right tail)
Points curve downward (below line at right tail)	Left-skewed (heavy left tail)
S-shaped curve	Data are more spread out or less variable than the reference distribution
Large deviations at ends (tails)	Outliers or heavy tails compared to the normal distribution

Why It’s Useful

Tests whether your data are normally distributed (normality check).
Detects skewness, kurtosis, and outliers.
Helps decide whether parametric statistical tests (which assume normality) are appropriate.
Commonly used before applying regression, ANOVA, or t-tests.