Class 11

Math

JEE Main Questions

Statistics

The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.

$x=n∑x_{i} $

$860+a+b =9$

$a+b=12$

$σ_{2}=n∑(x−x)_{2} $

$=83_{2}+4+1+9+16+(a−9)_{2}+(b−9)_{2} $

$=9.25$

$39+(a−9)_{2}+(b−9)_{2}=74$

$a_{2}+b_{2}−18(a+b)+162=35$

$a_{2}+b_{2}−216+162=26$

$a_{2}+b_{2}=80$ eqn(1)

$a+b=12$ eqn(2)

when a=8 , b=4

when a=4, b=8