How is the mean calculated from a set of data values?

In statistics, the arithmetic mean—often referred to simply as the average—is the most common way to designate the central value of a set of data.12

To calculate the arithmetic mean of a set of $n$ numbers ($x_1,x_2,\dots ,x_n$), you add all the values together and divide the resulting sum by the total count of numbers in the set. Mathematically, this is expressed as:12

$$\overline{x}=\frac{{\sum }_{i=1}^n{x}_i}{n}$$

For data that is grouped into intervals, the calculation differs: you use a weighted arithmetic mean where each value ($x_i$) represents the midpoint of an interval, and its corresponding weight ($w_i$) is the number of data points within that specific interval. The weighted mean is determined by calculating the sum of the products of the values and their weights, then dividing by the total sum of the weights.12