How do you find the average from a frequency table?

To find the average from a frequency table, you need to follow a systematic approach that incorporates both the frequency of each category and the corresponding values. The method involving the addition of a third column, often labeled as (fx), is crucial.

In this method, you will multiply each category value by its frequency to get the total contribution of each category to the overall sum. This is where the (fx) column comes into play; it represents these products. Once you have calculated the totals for the (fx) column, you then aggregate these values to find the total sum for all categories.

After obtaining the total sum from the (fx) column, you divide this sum by the total number of observations, which is the sum of all the frequencies. This will give you the average value of the data represented in the frequency table.

Using this approach ensures that each category's influence on the average is accurately reflected according to how many times that category occurs.