Question

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

Answer 1

Answer: (B)

$a=3,b=4$

Mean $=\frac{(a+b+8+5+10)}{5}=6$
$\Rightarrow a+b+23=30\Rightarrow a+b=7$ ...(i)
Varience$=\frac{2a^2+b^2+64+25+100}{5}-{\left(mean\right)}^2=6.8$
$\Rightarrow \frac{2a^2+b^2+89}{5}-36=6.8$
$\Rightarrow a^2+b^2=25$ ...(ii)
From (i) and (ii),
$a=3,b=4$ or $a=4,b=3$