Question

Let in a series $2n$ observations, half of them are equal to $a$ and remaining half are equal to $-a$. Also by adding a constant $b$ in each of these observations, the mean and standard deviation of new set become $5$ ad $20$, respectively. Then the value of $a^2+b^2$ is equal to

• A. $250$
• B. $925$
• C. $650$
• D. $425$

Answer 1

The correct option is D $425$

Given series is $a\left(n\text{times}\right),-a\left(n\text{times}\right)$
$\overline{x}=0$
If $b$ is added to each of them, then the new mean is
$\overline{x^{\prime }}=\overline{x}+b\Rightarrow b=5$

Standard deviation deosn't change when same number is added to all, so
$\sqrt{\frac{n{a}^2+n{a}^2}{2n}-0}=20\Rightarrow a^2=400\therefore a^2+b^2=425$