Question

Mean age of $25$ members of a club was $38$ years. If $5$ members with mean age of $42$ years have left the club, what is the present mean age of the club members?

Answer 1

Mean age of $25$ members was $38$ years.

$\therefore n=25$

$\overline{x}=38$

$\overline{x}=\frac{\sum x}{n}$

$\sum x=\overline{x}\times n=25\times 38=950$

Sum of all $25$ members age is $950$ years.

Now, $5$ members with mean $42$ years leave, then

$n=5$

$\overline{y}=42$

$\overline{x}=\frac{\sum y}{n}$

$\sum y=\overline{y}\times n=42\times 5=210$ $years.$

So, sum of age of remaining 20 members are, $950-210=740$ $years.$

$\therefore$ $\sum z=740$

$n=20$

New mean, $\overline{z}=\frac{\sum z}{n}=\frac{740}{20}=37$ $years.$