Given paired data
\begin{equation*}
(x_1,y_1), (x_2,y_2), ... , (x_n,y_n)
\end{equation*}
with corresponding means \(\overline{x}\) and \(\overline{y}\text{,}\) the sample covariance is given by
\begin{equation*}
s_{xy} = \sum_{k=1}^n \frac{(x_k-\overline{x})(y_k-\overline{y})}{n-1}.
\end{equation*}