Question

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 :

• A. -20
• B. -5
• C. 10
• D. -10

Answer 1

Answer: (A)

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