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  • 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 isOption:

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

Option: 1

1216


Option: 2

1072


Option: 3

1456


Option: 4

1792


Answers (1)

best_answer

Let remaining two observations are a and b

\begin{aligned} & 5=\frac{1+3+5+a+b}{5} \\ & \Rightarrow \mathrm{a}+\mathrm{b}=16 \ldots(\mathrm{i}) \\ & 8=\frac{1^2+3^2+5^2+a^2+b^2}{5}-25 \\ & \Rightarrow \mathrm{a}^2+\mathrm{b}^2=130 \\ & \mathrm{a}^2+\mathrm{b}^2=130 \ldots(\mathrm{ii}) \\ & \begin{aligned} (\mathrm{a}+\mathrm{b})^2=\mathrm{a}^2+\mathrm{b}^2+2 \mathrm{ab} \\ \Rightarrow 256=130+2 \mathrm{ab} \\ \mathrm{ab}=63 \\ \mathrm{a}^3+\mathrm{b}^3=(\mathrm{a}+\mathrm{b})^3-3 \mathrm{ab}(\mathrm{a}+\mathrm{b}) \\ \quad=(16)^3-3(63)(16) \\ \quad=4096-3024 \end{aligned} \\ & \Rightarrow \mathrm{a}^3+\mathrm{b}^3=1072 \end{aligned}

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SANGALDEEP SINGH

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