QJEEM23Ma1fb4: JEE Main 2023 Mathematics - Class 11 JEEM23Ma1fb4 Solution: The mean and variance of 7 observations are 8 and 16…

$\sum {{x_i} = 7 \times 8 = 56}$

${{\sum {x_i^2} } \over n} - {\left( {{{\sum {{x_i}} } \over n}} \right)^2} = 16$

${{\sum {x_i^2} } \over 7} - 64 = 16$

$\sum {x_i^2 = 560}$

when 14 is omitted

$\sum {{x_i} = 56 - 14 = 42}$

New mean $= a = {{\sum {{x_i}} } \over 6} = 7$

$\sum {x_i^2 = 560 - 196 = 364}$

new variance, $b = {{\sum {x_i^2} } \over 6} - {\left( {{{\sum {{x_i}} } \over 6}} \right)^2}$

$= {{364} \over 6} - 49 = {{35} \over 3}$

$3b = 35$

$a + 3b - 5 = 7 + 35 - 5 = 37$