JEE MAIN - Mathematics (2024 - 29th January Morning Shift - No. 22)
If the mean and variance of the data $$65,68,58,44,48,45,60, \alpha, \beta, 60$$ where $$\alpha> \beta$$, are 56 and 66.2 respectively, then $$\alpha^2+\beta^2$$ is equal to _________.
Answer
6344
Explanation
$$\begin{aligned}
& \overline{\mathrm{x}}=56 \\
& \sigma^2=66.2 \\
& \Rightarrow \frac{\alpha^2+\beta^2+25678}{10}-(56)^2=66.2 \\
& \therefore \alpha^2+\beta^2=6344
\end{aligned}$$
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