---
tag: 8GZJQBPBY0
kind: concept
name: Directional statistics
msc: [62H11]
sources:
  - url: https://en.wikipedia.org/wiki/Directional_statistics
same_as:
  wikidata: Q3497519
  wikipedia: Directional statistics
---

## Summary

Directional statistics is the part of statistics whose observations are directions, angles or rotations.
Such data live on the circle, on a [[sphere|T62369RFH6]] or on other manifolds, not on a line, so the usual mean and variance can mislead.
Means are taken of unit vectors instead of angles, and models such as the [[von Mises–Fisher distribution|V8ZZ7A2FMF]] replace the normal distribution.
Applications include wind directions, animal navigation, times of day and orientations of rocks.

## Explanations

### L1 human

Two wind directions of $350$ and $10$ degrees both point almost due north.
Their ordinary average is $180$ degrees, due south, which is plainly wrong.
Directional statistics treats each direction as an arrow of length $1$ and adds the arrows.
The sum of these two arrows points due north, the sensible answer.