Question

The mean of the numbers $a,b$, 8, 5, 10 is 6 and the variance is $6.8$ 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

The correct option is B $a=3,b=4$

Variance is $\frac{\sum x^2}{n}-{\left(\frac{\sum x}{n}\right)}^2=6.8$ and $\left(\frac{\sum x}{n}\right)=6$ (given)
$=>\frac{a^2+b^2+64+25+100}{5}-36=6.8=>a^2+b^2+9=34.0=>a^2+b^2=25$

$3^2+4^2=5^2=25$

so $a=3,b=4$ thus option B is correct.