This GCSE Maths histograms worksheet with answers is designed for focused GCSE revision. Histograms are different from bar charts because the area represents frequency. The key formula is frequency density = frequency / class width.
Use it as a short practice task before moving into mixed exam questions. If you need more structured help, I also offer GCSE Maths tutoring and parent-friendly GCSE revision support.
Before you start
The level for this worksheet is Higher. Work through the questions without checking the answers first. The point is not only to get the final answer, but to practise the method clearly enough that you could repeat it in a test.
Keep your working visible. GCSE Maths mark schemes often reward method, so a clear first line can still matter even if the arithmetic goes wrong later.
Skills this worksheet checks
This worksheet checks whether you can recognise common histograms question types, choose a sensible first step, and keep your working organised. Those three habits matter more than racing through the list.
For each question, write one line that explains the method before you calculate. That might be a formula, a common denominator, an equation, a route through a diagram, or the probability operation you are using. This makes the practice closer to the way marks are awarded in GCSE exams.
Worksheet questions
- A class interval has width 10 and frequency 30. Find the frequency density.
- A bar has width 5 and frequency density 4. Find the frequency.
- A group 20 <= x < 40 has frequency 50. Find the frequency density.
- A bar from 0 to 8 has density 6. Find the frequency.
- A class has frequency 18 and density 3. Find the class width.
- Intervals 0-10 and 10-30 have frequencies 20 and 50. Find both densities.
- A histogram bar has area 36 and width 12. Find the density.
- A class 40 <= x < 70 has density 1.6. Find the frequency.
- The total frequency is 120. Known bar areas total 95. Find the missing frequency.
- A bar has width 15 and frequency 24. Find the density.
Answers and method checks
| # | Question | Method | Answer |
|---|---|---|---|
| 1 | A class interval has width 10 and frequency 30. Find the frequency density. | 30 divided by 10. | 3 |
| 2 | A bar has width 5 and frequency density 4. Find the frequency. | Area is width x density. | 20 |
| 3 | A group 20 <= x < 40 has frequency 50. Find the frequency density. | Class width is 20, so 50/20. | 2.5 |
| 4 | A bar from 0 to 8 has density 6. Find the frequency. | 8 x 6. | 48 |
| 5 | A class has frequency 18 and density 3. Find the class width. | Width = frequency / density. | 6 |
| 6 | Intervals 0-10 and 10-30 have frequencies 20 and 50. Find both densities. | Divide each frequency by its own class width. | 2 and 2.5 |
| 7 | A histogram bar has area 36 and width 12. Find the density. | Area/width = density. | 3 |
| 8 | A class 40 <= x < 70 has density 1.6. Find the frequency. | Width 30 times density 1.6. | 48 |
| 9 | The total frequency is 120. Known bar areas total 95. Find the missing frequency. | Total histogram area equals total frequency. | 25 |
| 10 | A bar has width 15 and frequency 24. Find the density. | 24/15 = 1.6. | 1.6 |
How to mark this worksheet
Mark each question with more detail than a tick or cross. If the answer is wrong, label the error: method choice, arithmetic, notation, units, signs, calculator input, or not reading the question carefully.
For histograms, it is especially useful to redo the questions you missed after a short break. A topic can feel familiar immediately after reading the answer, but the real test is whether you can start the method independently later.
A good correction is specific. Instead of writing 'revise this', write the exact fix: choose a common denominator, show the multiplier, update the probability after the first choice, label the radius, or subtract the smaller coordinate from the larger one. Specific corrections make the next practice session much easier to plan.
Common mistakes
- Using bar height as frequency.
- Ignoring unequal class widths.
- Reading the end points incorrectly.
- Forgetting that area, not height, gives frequency.
Extension practice
After marking the worksheet, choose three questions and change one number in each. Keep the structure the same, then solve your new versions. This is a quick way to check whether you understand the method rather than remembering the original answer.
If the changed question becomes much harder, that is useful information. It usually means the method is not fully secure yet, or that a small change has introduced a new skill such as negative numbers, fractions, unit conversion, exact form, or a second step.
Students aiming for higher grades should also write one short explanation question. For example: explain why this vector is parallel, explain why these two routes must be added, explain why this theorem applies, or explain why the original amount is not the same as the sale amount. These explanations build the reasoning marks that many students miss.
What to practise next
Once you can complete this worksheet accurately, move to mixed questions where the topic is not written in the title. That is closer to the exam, because you have to recognise the method as well as carry it out.
You can also use the Maths practice papers hub to connect topic practice with broader exam-style work. If the same mistake keeps appearing, bring that exact question to a lesson or send it to me so we can work out what is blocking the method.
