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  4. The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations Ls multiplied by p and then reduced by q where p ≠ 0 and q ≠ 0. If the new mean and new s.d . become half of their original values, then q is equal to :

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Q. The mean and the standard deviation (s.d.) of $10$ observations are $20$ and 2 respectively. Each of these $10 $ observations Ls multiplied by $p$ and then reduced by $q$ where $p \ne 0 $ and $q \ne 0$. If the new mean and new $s.d$ . become half of their original values, then $q$ is equal to :

JEE MainJEE Main 2020Statistics

Solution:

$20p - q = 10\, ...\left(i\right)$
and $2\left|p\right|-1 \Rightarrow p=\pm \frac{1}{2}\,...\left(ii\right)$
so, $p=-\frac{1}{2}$ and $q=-20$