Question

The mean and variance of $5$ observations are $5$ and $8$ respectively. If $3$ observations are $1,3,5$, then the sum of cubes of the remaining two observations is

• A. 1216
• B. 1456
• C. 1072
• D. 1792

Answer 1

Answer: (C)

$\frac{1+3+5+a+b}{5}=5$
$a+b=16\dots \dots (1)$
${\sigma }^2=\frac{\sum x_1^2}{5}-{\left(\frac{\sum x}{5}\right)}^2$
$8=\frac{1^2+3^2+5^2+a^2+b^2}{5}-25$
$a^2+b^2=130\dots \dots (2)$
$\text{ by }(1),(2)$
$a=7,b=9$
$\text{ or }a=9,b=7$