At Level 2, averages questions go beyond ‘find the mean’: you are asked to calculate from a frequency table, estimate the mean from grouped data, and – the part worth the most marks – compare two data sets and say what the numbers mean. This free worksheet covers all of it in nine exam-style questions with worked answers.
Free to download, print and share for personal or classroom use. Answers included.
What’s in this worksheet
- Remember box: mean, median, mode, range, and the midpoint method for grouped data
- Section A – raw data: a receptionist’s call log, a misleading ‘average wage’, a new student joining a class (12 marks)
- Section B – a frequency table of cars per household: mode, median and mean (5 marks)
- Section C – grouped pharmacy waiting times: complete the table, estimate the mean, find the median group, judge the target (7 marks)
- Section D – comparing two delivery drivers and two mock-test groups using mean and range (6 marks)
- Worked answers with the reasoning examiners want in ‘compare’ questions
Common mistakes on this topic
From our tutors’ marking and the most recent examiner reports – check your work against these:
- Forgetting to put the data in order before finding the median.
- Dividing by the number of groups instead of the total frequency in a table.
- Comparing data sets by quoting numbers only – you must say what the numbers mean (e.g. “more consistent”).
How to use it
- Print the worksheet (or work on screen) and attempt every question without looking at the answers. Give yourself a rough time limit – Level 2 exams are tight.
- Mark your work against the answer page. For maths, check the method as well as the final number; method marks are where most of the marks are.
- Read the ‘common mistakes’ notes below and check whether any of them happened to you. Then redo the questions you got wrong a day later.
Related free resources
- Functional Skills Maths Level 2 Percentages Worksheet
- Functional Skills Maths Level 2 Ratio and Proportion Worksheet
- All free Functional Skills Maths Level 2 resources
Frequently asked questions
How do you estimate the mean from a grouped frequency table?
Find the midpoint of each group, multiply it by the group’s frequency, add those products up, and divide by the total frequency. It is an estimate because you don’t know the exact values within each group.
Which average should I use?
The mean uses every value but is pulled by outliers; the median is the middle value and is fairer when there is an extreme value (like one very high salary); the mode is the most common value and works for categories. Exam questions often ask you to say which is more representative and why.
What does the range tell you?
How spread out the data is – biggest minus smallest. A small range means consistent results; a large range means they vary a lot. In ‘compare two sets’ questions, always mention the range as well as the average.
Want a tutor to mark your work? Not sure where you stand? Take the free 15-minute mini mock test. Ready to get qualified? Our live 10-week Functional Skills Level 2 Maths course runs in small groups with a mock exam included, and the 5-day revision course is there if your exam is close.