Here we will learn about the mean from a frequency table, including what it is and how to calculate it. We will also learn how to find an estimate for the mean from a grouped frequency table.
There are also averages from frequency tables worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
Mean from a frequency table is when we find the mean average from a data set which has been organised into a frequency table.
To calculate the mean we find the total of the values and divide the total by the number of values. The number of values is the total frequency. This can be abbreviated to n .
We can use an extra column to help.
Mean is a measure of central tendency, it is a value that can be used to represent a set of data.
E.g. The frequency table shows the number of people living in 16 flats.
There are 5 flats with 1 person living there, so we work out 1\times5=5
There are 6 flats with 2 people living there, so we work out 2\times6=12
There are 3 flats with 3 people living there, so we work out 3\times3=9
There are 2 flats with 4 people living there, so we work out 2\times4=8
The number of values (n) is the total frequency, here n=16
The mean is 2.125 people
When the data has been grouped together and put into a grouped frequency table we cannot find the actual mean because we only have a range of possible values.
Instead we can find an estimate for the mean using the midpoints of each group. We can add more columns to the grouped frequency table to help.
E.g.
The frequency table shows the marks scored in a test by 20 students.
There are 3 people who scored between 0-9 marks. As we don’t know the exact number of marks that each of these people scored we will use the midpoint of 4.5 marks.
We can find the midpoint by adding the smallest value and the largest value together and dividing by 2
The estimated mean is 21 marks
