3.8: Mean From a Frequency Distribution
Sometimes, data gathered from an experiment on a large sample or population are organized into concise tables. In such cases, the frequency of the quantitative data set is plotted in the form of a table. Or else, the data values are grouped into the quantity’s intervals, which form classes, and their respective frequencies are known. That is, the data values are distributed over different categories or classes. This is known as frequency distribution.
When such a data set is encountered, the arithmetic mean can be calculated by considering each class as an element. Each category represents a quantity or an average quantity, and its frequency gives its weight for computing the mean.
The total number of points in the sample or population is thus the sum of the frequencies of the individual classes. Hence, the mean from a frequency distribution comprises the sum of the distribution’s frequencies in its denominator.
The mean calculated from a frequency table can be considered a weighted mean, where the weight refers to the frequency of each class.