---
tag: ZP455BADJ3
kind: concept
name: Sample mean and sample covariance
msc: [62H12, 62F10]
sources:
  - url: https://en.wikipedia.org/wiki/Sample_mean_and_covariance
same_as:
  wikidata: Q2348165
  wikipedia: Sample mean and covariance
---

## Summary

The sample mean and the sample covariance matrix summarise a sample of vectors by its centre and its spread.
They are the multivariate versions of the [[sample mean|03Y6AQ2S0J]] and the [[sample variance|0NHXGY2C5J]].
They are unbiased estimators of the mean vector and the [[covariance matrix|0V7G6WMFK0]], and they are the starting point of multivariate analysis.

## Explanations

### L1 human

Measure the height and the weight of each person in a group.
The sample mean is the average point: average height and average weight.
The sample covariance matrix records how much each quantity varies, and whether tall people tend to be heavy.
For the two points $(0, 0)$ and $(2, 2)$, the mean is $(1, 1)$, and both coordinates vary together, so the off-diagonal entry is positive.