What is the method for finding the average from a grouped frequency table?

To find the average from a grouped frequency table, the method involves calculating the mid-interval values for each group, which represent the center of each interval. Once these mid-interval values are determined, they are multiplied by the frequency of each interval, resulting in a new column called "frequency times mid-interval value". This product gives a weighted contribution to the total for each interval.

The next step is to sum these products to get a total value that reflects the weighted average based on the frequencies. Finally, you divide this total by the overall sum of the frequencies to arrive at the average. This process accurately accounts for the distribution of data across the intervals and provides a meaningful average based on the frequency of each group.

This method is crucial because it utilizes both the frequency and the data values effectively, rather than relying on less accurate means such as just taking the highest frequency or simply averaging mid-interval values without consideration of their frequencies.