Let X={11,12,13, …, 40,41} and Y={61,62,63, …, 90,91} be the two sets of observations. If x̄ and ȳ are their respective means and σ^2 is the…

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