Statistics Question 5
Question 5 - 2024 (29 Jan Shift 1)
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
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Answer (6344)
Solution
$\overline{x}=56$
$\sigma^{2}=66.2$
$\Rightarrow \frac{\alpha^{2}+\beta^{2}+25678}{10}-(56)^{2}=66.2$
$\therefore \alpha^{2}+\beta^{2}=6344$
