Q47 / 105 · JEE Main 2008 · Mathematics

The mean of the numbers $a, b, 8,5,10$ is 6 and the variance is $6.80$. Then which one of the following gives possible values of $a$ and $b$ ?

  • A
    $a=0, b=7$
  • B
    $a=5, b=2$
  • C
    $a=1, b=6$
  • Correct answer
    D
    $a=3, b=4$

Solution

Mean of $a, b, 8,5,10$ is 6 $$ \begin{aligned} & \Rightarrow \frac{a+b+8+5+10}{5}=6 \\ & \Rightarrow a+b=7 \end{aligned} $$ Given that Variance is $6.8$ $$ \begin{aligned} & \therefore \text { Variance }=\frac{\sum\left(\mathrm{X}_{\mathrm{i}}-\mathrm{A}\right)^2}{\mathrm{n}} \\ & =\frac{(\mathrm{a}-6)^2+(\mathrm{b}-6)^2+4+1+16}{5}=6.8 \end{aligned} $$ $$ \begin{aligned} & \Rightarrow a^2+b^2=25 \\ & a^2+(7-a)^2=25 \\ & \Rightarrow a^2-7 a+12=0 \\ & \therefore a=4,3 \text { and } b=3,4 \end{aligned} $$

Hence, the correct answer is option: 'D'.

Relevant Questions