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13.Statistics
hard
The mean and the standard deviation (s.d.) of $10$ observations are $20$ and $2$ resepectively. Each of these $10$ observations is multiplied by $\mathrm{p}$ and then reduced by $\mathrm{q}$, where $\mathrm{p} \neq 0$ and $\mathrm{q} \neq 0 .$ If the new mean and new s.d. become half of their original values, then $q$ is equal to
A
$-20$
B
$10$
C
$-10$
D
$-5$
(JEE MAIN-2020)
Solution
$20 \mathrm{p}-\mathrm{q}=10\ldots(i)$
and $2|p|=1 \Rightarrow p=\pm \frac{1}{2}\ldots(ii)$
so, $\mathrm{p}=-\frac{1}{2}$ and $\mathrm{q}=-20$
Standard 11
Mathematics
