Important: The stats package has been deprecated. Use the superseding package Statistics instead.

The function covariance of the subpackage stats[describe, ...] computes the covariance between two statistical lists.

The two data lists must have the same number of observations, with the same weights for each corresponding elements.

Let x[i] be the observations of data1, y[i] be the observations of data2, xmean be the mean of data1, ymean be the mean of data2 and N be the common number of observations. Then the covariance is defined to be $\frac{\sum _{i=1}^N\left(x_i-\mathrm{xmean}\right)\left(y_i-\mathrm{ymean}\right)}{N}$.

If either of x[i] and y[i] is missing, then the corresponding term in the above sum is omitted.

The covariance is used in the computation of the linear correlation. Refer to describe[linearcorrelation] for more information.

Classes are assumed to be represented by the class mark, for example 10..12 has the value 11.

$\mathrm{with}\left(\mathrm{stats}\right)\:$

$\mathrm{data1}≔\left[\mathrm{Weight}\left(3\,10\right)\,4\,\mathrm{Weight}\left(11\,3\right)\right]$

$\mathrm{data1}≔\left[\mathrm{Weight}\left(3\,10\right)\,4\,\mathrm{Weight}\left(11\,3\right)\right]$

$\mathrm{data2}≔\left[\mathrm{Weight}\left(1\,10\right)\,3\,\mathrm{Weight}\left(12\,3\right)\right]$

$\mathrm{data2}≔\left[\mathrm{Weight}\left(1\,10\right)\,3\,\mathrm{Weight}\left(12\,3\right)\right]$

$\mathrm{describe}\left[\mathrm{covariance}\right]\left(\mathrm{data1}\,\mathrm{data2}\right)$

$\frac{407}{28}$