Question

The mean of a set of numbers is $\bar{x}$. If each item is decreased by $4$, then mean of new observations (set) is

• A. unaltered
• B. raised by $4$ units in $\bar{x}$
• C. reduced by $4$ units in $\bar{x}$
• D. None of these

Answer 1

Answer: (C)

Let the n numbers are $x_1$, $x_2$, $x_3$, ..., $x_n$
$\therefore$ New items are $x_1-4$, $x_2-4$, $x_3-4$ ,..., $x_n-4$
$\therefore$ New mean $=\frac{\left(x_1-4\right)+\left(x_2-4\right)+...+\left(x_n-4\right)}{n}$
$=\frac{x_1+x_2+...x_n-4n}{n}$
$=\frac{x_1+x_2+...x_n}{n}-4=\bar{x}-4$
So, new mean is reduced by $4$ units in $\bar{x}$