QJEEM23Mab15a: JEE Main 2023 Mathematics - Class 11 JEEM23Mab15a Solution: Let and be the two sets of observations. If and are their…

$x = \{ 11,12,13\,....,40,41\}$

$y = \{ 61,62,63\,....,90,91\}$

$\overline x = {{{{31} \over 2}(11 + 41)} \over {31}} = {1 \over 2} \times 52 = 26$

$\overline y = {{{{31} \over 2}(61 + 91)} \over {31}} = {1 \over 2} \times 152 = 76$

${\sigma ^2} = {{\sum {x_i^2 + \sum {y_i^2} } } \over {62}} - {\left( {{{\sum {x + \sum y } } \over {62}}} \right)^2}$

$= 705$

Now,

$\left| {\overline x + \overline y - {\sigma ^2}} \right|$

$= |26 + 76 - 705| = 603$