3.8:
Mean From a Frequency Distribution
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.
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.