Frequency Tables- Finding Averages

A frequency table is a method of organising raw data in a compact form, by displaying a series of data values and their corresponding frequencies.
The frequency in a frequency table refers to the number of times a particular value appears in the data set.
To find an average, you may calculate the mean, median, or mode of a data set.
The mean is calculated by adding up all the values, then dividing by the total number of values.
With a frequency table, to find the mean you need to multiply each value by its frequency to get a “weighted total”, then sum all these totals together, and divide by the total frequency. It is important not to divide by the number of values, because each value can appear more than once.
The median is the middle number when all the values are arranged in ascending order. If there is an even number of values, the median is the average of the two middle numbers.
With a frequency table, to find the median you need to find the cumulative frequency, which is the total frequency up to and including the current value. Then you find the value that has a cumulative frequency just over half of the total frequency.
The mode is the most frequently occurring value in a data set.
With a frequency table, the mode is just the value with the highest frequency.
Sometimes with grouped frequency tables, it may not be possible to determine the exact mean, median, or mode, but you can estimate them by using the midpoint of each group.
Each of these averages tell you something different about the data set, and none of them is inherently better or worse than the others. They all provide a summary of the data, but in different ways.
Practice on different data sets to understand the process and internalise the steps in calculating mean, median, and mode from frequency tables, this will greatly help grasp the techniques and concepts.