Definition:Sample Covariance

Definition

Let $S$ be a sample of $n$ paired observations $\tuple {x_i, y_i}$ for $i \in \set {1, 2, \ldots, n}$.

The sample covariance of $S$ is:

$c_{x y} = \ds \sum_{i \mathop = 1}^n \dfrac 1 n \paren {x_i - \hat x} \paren {y_i - \hat y}$

where $\hat x$ and $\hat y$ are the means of $\set {x_i: i \in \set {1, 2, \ldots, n} }$ and $\set {y_i: i \in \set {1, 2, \ldots, n} }$ respectively.

Also see

• Results about sample covariance can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): covariance
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): covariance