Question

The average of $50$ numbers is $38$. If two numbers $45$ and $55$ discarded, the average of the remaining set of numbers is

• A. $38.5$
• B. $37.5$
• C. $37.0$
• D. $36.5$

Answer 1

The correct option is B $37.5$

$n=50$

$\overline{x}=38$

$\sum x$=$n\times \overline{x}=50\times 38=1900$

if $45$ and $55$ discarded

$\sum x_{new}=1900-(45+55)=1800$

Now $n=48$

$\overline{x}=\frac{\sum x_{new}}{n}=\frac{1800}{48}=37.5$