Probability
3. Continuous Distributions
Q-Q Plots

Q-Q Plots and Normal Probability

A Quantile-Quantile (Q-Q) plot is a graphical tool to help us assess if a dataset came from some theoretical distribution such as a Normal or exponential.

If the data is perfectly normally distributed, the points will fall precisely on the straight 45-degree diagonal line.

Q-Q plot

Compare sample quantiles to theoretical normal quantiles. Deviations from the red line signal non-normality.

Skewness
Normal
Move away from 0 to create curvature in the Q-Q plot.

Test Your Knowledge

Example: Interpreting Q-Q Plots

You plot a dataset on a Normal Q-Q plot. The middle of the data closely hugs the 45-degree line, but the points on the far left dip below the line, and the points on the far right curve above the line. What does this indicate?

View Step-by-Step Solution

This specific "S-shape" curve indicates that the tails of your dataset are "heavier" or "fatter" than a normal distribution.

  • Points dipping below the line on the left mean the actual values are more extremely negative than expected.
  • Points curving above the line on the right mean the actual values are more extremely positive than expected.

The data likely follows a Heavy-Tailed distribution (like the Student's t-distribution) rather than a Normal distribution.