Question

Mean of $100$ observations is $50$ and S.D. is $10$. If $5$ is subtracted from each observation and then it is divided by $4$, then the new mean and S.D. are?

• A. $11.25,6.25$
• B. $11.25,2.5$
• C. $11.25,10$
• D. $11.35,3.5$

Answer 1

The correct option is B $11.25,2.5$

If a constant is added or substracted or multiplied or divided, the mean also changes similarly.

However, S.D. is not affected if the terms are increased or decreased by the same constant but changes similarly when each term is divided or multiplied by a constant.

$\therefore$ Here,

The new mean is $=\frac{50-5}{4}=\frac{45}{4}=11.25$

The new S.D is $=\frac{10}{4}=2.5$