Media derivante da distribuzione di frequenza

Generally, the arithmetic mean, or simply the mean, is calculated by dividing the sum of all the data values by the total number of values.  

But how is the mean from a frequency distribution determined, where repeated data values are grouped under different categories? 

First, multiply each data value with its corresponding frequency. Then, add them up and divide by the sum of the frequencies to get the mean value.

On the other hand, if the frequency distribution table has class intervals, their mean is calculated by first determining the class midpoints. 

For the class from 0 to 10, the midpoint is calculated by adding the boundary values and dividing them by 2. Similarly, calculate class midpoints of the remaining classes.

Thereafter, the midpoints and their corresponding frequencies are multiplied and added together, as denoted by sigma f x. Finally, these values are divided by the sum of all the frequencies denoted by sigma f. This gives the mean from the frequency distribution.