Question

Consider first $10$ positive integers having standard deviation $2.87$. If we multiply each number by $-1$ and then add $1$ to each number, the standard deviation of the numbers so obtained is

• A. $8.25$
• B. $2.87$
• C. $-2.87$
• D. $-8.25$

Answer 1

The correct option is B $2.87$

We know that $S.D(ax+b)=|a|.S.D\left(x\right)$
Here, $a=-1,b=1$
$\therefore$ Required standard deviation $=|-1|\times 2.87=2.87$