Mathematics Question from JEE Main 2023 · 29 January, Shift 2

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