QJEEM22Ma2435: JEE Main 2022 Mathematics - Class 11 JEEM22Ma2435 Solution: The mean and standard deviation of 40 observations are 30 and 5 …

$\mu = {{\sum {{x_i}} } \over {40}} = 30 \Rightarrow \sum {{x_i} = 1200}$

${\sigma ^2} = {{\sum {x_i^2} } \over {40}} - {(30)^2} = 25 \Rightarrow \sum {x_i^2 = 37000}$

After omitting two wrong observations

$\sum {{y_i} = 1200 - 12 - 10 = 1178}$

$\sum {y_i^2 = 37000 - 144 - 100 = 36756}$

Now ${\sigma ^2} = {{\sum {y_i^2} } \over {38}} - {\left( {{{\sum {{y_i}} } \over {38}}} \right)^2}$

$= {{36756} \over {38}} - {\left( {{{1178} \over {38}}} \right)^2} = - {31^2}$

$= 38{\sigma ^2} = 36756 - 36518 = 238$