The mean of 24 numbers is 35.

Question:

The mean of 24 numbers is 35. If 3 is added to each number, what will be the new mean?

Solution:

Let the numbers be x1x2,...x24.

We know:

Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$

Thus, we have:

$35=\frac{x_{1}+x_{2}+\ldots \ldots \ldots+x_{24}}{24}$

$\Rightarrow 840=x_{1}+x_{2}+\ldots \ldots+x_{24} \ldots \ldots$ (i)

After addition, the new numbers become $\left(x_{1}+3\right),\left(x_{2}+3\right), \ldots\left(x_{24}+3\right)$

New mean:

$=\frac{\left(x_{1}+3\right)+\left(x_{2}+3\right)+\ldots \ldots \ldots+\left(x_{24}+3\right)}{24}$

$=\frac{\left(x_{1}+x_{2}+\ldots \ldots \ldots+x_{24}\right)+(24 \times 3)}{24}$

$=\frac{840+72}{24} \quad[$ From $(\mathrm{i})]$

$=\frac{912}{24}$

$=38$