Statistics

Let \(X=\{11,12,13,....,40,41\}\) and \(Y=\{61,62,63,....,90,91\}\) be the two sets of observations. If \(\overline x\) and \(\overline y\) are their respective means and \(\sigma^2\) is the variance of all the observations in \(\mathrm{X\cup Y}\), then \(\left| {\overline x + \overline y - {\sigma ^2}} \right|\) is equal to ____________.