Averages From Frequency Table Worksheet

Averages from frequency table at a glance

Given a table of data, we can find the mean, median, mode and range of the data set. For example, this table shows the number of goals scored in 21 football matches:

Number of Goals               Frequency

0                                            5

1                                            4

2                                           7

3                                           4

• The mode is the most common number of goals scored. The number of goals with the highest frequency is 2 and so the mode = 2.
• The median is the middle value. In this case it is the 11th value, which would be 2. 
• To find the mean number of goals, we multiply the number of goals by their frequency, add these totals (30) and divide by the total number of games (21). The mean is therefore 1.4.
• The range is the difference between the highest and lowest number of goals. 3 subtract 0 is equal to 3. 

We can also find averages from a grouped frequency table, where data is arranged into groups. The class intervals for grouped data are often denoted using inequalities. For example, the classes of data about the shoe size, s, of a number of people could be 1≤s<4, 4≤s<7, and 7≤s<10.

 For grouped data: 

• The modal class is the class with the highest frequency.
• The class which contains the median which is the class in which the middle value lies.
• To find the estimated mean, we multiply the midpoint of each class by its frequency, add these together and divide by the total number of items included in the table. 

You may be asked to find missing numbers in a frequency table using averages.

Looking forward, students can then progress to additional Statistics worksheets, for example a mean, median, mode and range worksheet or pie chart worksheet.

For more teaching and learning support on Statistics our GCSE maths lessons provide step by step support for all GCSE maths concepts.