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 :
Solution
Let observation $1,3,5, a, b$
<br/><br/>$$
\begin{aligned}
& \text { Mean } = \frac{9+a+b}{5}=5 \\\\
& \text { Variance } = \frac{a^{2}+b^{2}+35}{5}-25=8 \\\\
& \Rightarrow a+b=16 \text { and } a^{2}+b^{2}=130 \\\\
& \therefore a \text { and } b \text { are } 7 \text { and } 9 \\\\
& \therefore a^{3}+b^{3}=7^{3}+9^{3}=1072
\end{aligned}
$$
About this question
Subject: Mathematics · Chapter: Statistics · Topic: Measures of Central Tendency
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