Functional Skills: Estimating the Mean

Grouped Frequency Tables

Grouped frequency tables are a useful way of displaying broad data by grouping data into classes.

Example: the grouped frequency table below shows the number of exercise sessions attended by a group of people.

Note that the classes cannot overlap in a grouped frequency table – be careful when constructing grouped frequency tables not to put the same numbers in twice. For example, if the second class in the example above were 1-2, someone who attended 1 exercise session would fit into the first and second class.

In this example, all of the data is known but you may encounter other examples where the last class might say something like ‘10 or more’. This would also be useful if the data at the higher end was very spread out.

Estimating the Mean

We can use data from grouped frequency tables to estimate the mean value. The reason we are ‘estimating’ is because we do not know how the data is distributed in each class – it could all be at the lower end of the class, all at the higher end or evenly distributed throughout.

We estimate the mean by finding the midpoint of each class and assuming the midpoint to be an average value of each class. We then multiply the midpoint by the frequency, entering the values into a new column.

We can now estimate the mean by taking the total of the Midpoint \times Frequency column and dividing it by the total of the frequency column.

Mean = 85 \div 34 = 2.5

So the mean number of exercise sessions attended is 2.5