When data comes in groups – 0–10 minutes, 10–20 minutes – you cannot find the exact mean, but Level 2 expects you to estimate it using midpoints. It is a five-step method worth four or five marks, and this free worksheet takes you through it on the kind of tables the exam uses: waiting times, ages, spending and journey lengths.
Free to download, print and share for personal or classroom use. Answers included.
What’s in this worksheet
- Section A – The method (8 marks)
- Section B – In context (15 marks)
- Revise box with the rules and methods for the topic
- Worked answers for every question
Common mistakes on this topic
From our tutors’ marking and the most recent examiner reports – check your work against these:
- Dividing by the number of groups (4) instead of the total frequency (40).
- Using the group’s upper or lower bound instead of the midpoint.
- Giving the modal class as the highest frequency (16) instead of the group (4 ≤ t < 8).
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
- Comparing Data Sets Worksheet – Functional Skills Maths Level 2
- Reading and Drawing Charts and Graphs Worksheet – Functional Skills Maths Level 2
- Level 2 Maths Mini Practice Paper 1 – Functional Skills Maths Level 2
- All free Functional Skills Maths Level 2 resources
Frequently asked questions
How do you estimate the mean from a grouped frequency table?
Find each group’s midpoint, multiply by its frequency, add those products, and divide by the total frequency. For the bank table: (2 × 9 + 6 × 16 + 10 × 11 + 14 × 4) ÷ 40 = 7 minutes.
Why can you only estimate the mean from grouped data?
Because you don’t know the individual values – only which group each one is in. Assuming every value sits at the midpoint of its group gives a reasonable estimate, but not the exact mean.
What is the modal class?
The group with the highest frequency. Write down the group itself (e.g. 4 ≤ t < 8), not the frequency number.
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.