JEE PYQ: Statistics Question 7
Question 7 - 2021 (26 Feb Shift 2)
Let $X_1, X_2, \ldots, X_{18}$ be eighteen observations such that $\sum_{i=1}^{18}(X_i - \alpha) = 36$ and $\sum_{i=1}^{18}(X_i - \beta)^2 = 90$, where $\alpha$ and $\beta$ are distinct real numbers. If the standard deviation of these observations is 1, then the value of $|\alpha - \beta|$ is
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Answer: 4
Solution
$(\alpha - \beta)(\alpha - \beta + 4) = 0$. Since $\alpha \neq \beta$, $|\alpha - \beta| = 4$.
BETA
