QJEEM16Ma41ff: JEE Main 2016 Mathematics - Class 11 JEEM16Ma41ff Solution: The mean of 5 observations is 5 and their variance is 124. If…

Let 5 observations are x₁, x₂, x₃, x₄, x₅

given,   x₁ = 1, x₂ = 2, x₃ = 6

Mean = 5

$\therefore$    Mean $\left( {\overline x } \right)$ = ${{{x_1} + {x_2} + {x_3} + {x_4} + {x_5}} \over 5}$ = 5

$\Rightarrow$    1 + 2 + 6 + x₄ + x₅ = 25

$\therefore$    x₄ + x₅ = 16

$\Rightarrow$    (x₄ $-$ 5) + (x₅ $-$ 5) + 10 = 16

$\Rightarrow$    (x₄ $-$ 5) + (x₅ $-$ 5) = 6

$\therefore$    Mean deviation about mean,

=    ${{\sum {\left| {{x_i} - \overline x } \right|} } \over n}$

=    ${{\left| {1 - 5} \right| + \left| {2 - 5} \right| + \left| {6 - 5} \right| + \left| {{x_4} - 5} \right| + \left| {{x_5} - 5} \right|} \over 5}$

=    ${{4 + 3 + 1 + 6} \over 5}$

=     ${{14} \over 5}$

=   2.8