The mean and variance of 5 observations are 5 and 8 respectively.

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

Accepted Answer

Let observation $1,3,5, a, b$

$$
\begin{aligned}
& \text { Mean } = \frac{9+a+b}{5}=5 \\
& \text { Variance } = \frac{a^{2}+b^{2}+35}{5}-25=8 \\
& \Rightarrow a+b=16 \text { and } a^{2}+b^{2}=130 \\
& \therefore a \text { and } b \text { are } 7 \text { and } 9 \\
& \therefore a^{3}+b^{3}=7^{3}+9^{3}=1072
\end{aligned}
$$

Solutions · 1