marks	10-20	20-30	30-40	40-50	50-60
Frequency	4	10	20	40	50

The following frequency distribution shows the marks obtained by 124 students in Economics at a certain school. Find the arithmetic mean (rounding up to the nearest integer) using the direct method.

The sum of the values of all the observations $=f_1{x}_1+f_2{x}_2+\dots +f_n{x}_n$, and the number of observations $=f_1+f_2+\dots +f_n$.

So, the mean $\overline{x}$of the data is given by

$\overline{x}=\frac{f_1{x}_1+f_2{x}_2+\cdots +f_n{x}_n}{f_1+f_2+\cdots +f_n}$

According to the table

 $\Sigma {\text{f}}_{\text{i}}=124$          $\Sigma {\text{f}}_{\text{i}}{\text{x}}_{\text{i}}=5560$

$\text{Mean }=\frac{\Sigma {\text{f}}_{\text{i}}{\text{x}}_{\text{i}}}{\Sigma {\text{f}}_{\text{i}}}$

$=\frac{5560}{124}=44.83\simeq 45\text{ marks }$