JEE MAIN - Mathematics (2023 - 1st February Morning Shift - No. 8)
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 :
1792
1216
1456
1072
Explanation
Let observation $1,3,5, a, b$
$$ \begin{aligned} & \text { Mean } = \frac{9+a+b}{5}=5 \\\\ & \text { Variance } = \frac{a^{2}+b^{2}+35}{5}-25=8 \\\\ & \Rightarrow a+b=16 \text { and } a^{2}+b^{2}=130 \\\\ & \therefore a \text { and } b \text { are } 7 \text { and } 9 \\\\ & \therefore a^{3}+b^{3}=7^{3}+9^{3}=1072 \end{aligned} $$
$$ \begin{aligned} & \text { Mean } = \frac{9+a+b}{5}=5 \\\\ & \text { Variance } = \frac{a^{2}+b^{2}+35}{5}-25=8 \\\\ & \Rightarrow a+b=16 \text { and } a^{2}+b^{2}=130 \\\\ & \therefore a \text { and } b \text { are } 7 \text { and } 9 \\\\ & \therefore a^{3}+b^{3}=7^{3}+9^{3}=1072 \end{aligned} $$
Comments (0)
