Knowledge Organiser: Histograms
Part of Histograms · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Histograms within Histograms for GCSE Mathematics. Revise Histograms in Statistics for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 10 of 10 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 10 of 10
Practice
14 questions
Recall
12 flashcards
Knowledge Organiser: Histograms
Key Terms
- Histogram: A chart for continuous grouped data where area represents frequency
- Frequency density: Frequency ÷ class width — plotted on the y-axis
- Class width: The size of each interval (upper boundary − lower boundary)
- Modal class: The class interval with the highest frequency density
- Continuous data: Data that can take any value — no gaps between bars
- Skew: The shape of the distribution — positive (tail right), negative (tail left)
Must-Know Facts
- Histograms have NO gaps between bars — this distinguishes them from bar charts
- The y-axis shows frequency density, NOT frequency
- The area of each bar equals the frequency for that class
- For equal class widths, the tallest bar is the modal class
- For unequal class widths, compare frequency density — not bar height — to compare frequencies
- Total frequency = sum of all bar areas (frequency density × class width for each bar)
- Always use class boundaries (not midpoints) on the x-axis
Key Formulas
- Frequency density = Frequency ÷ Class width
- Frequency = Frequency density × Class width
- Area of bar = Frequency (this is the key relationship)
- Estimated mean = Σ(midpoint × frequency) ÷ Σfrequency
Common Mistakes
- Plotting frequency on y-axis: Histograms use frequency DENSITY (= frequency ÷ class width) on the y-axis, not frequency
- Equal class widths assumed: If class widths differ, bars must have different heights — frequency density corrects for this
- Area = frequency: The area of each bar equals the frequency — height alone does not represent frequency
- Gaps between bars: Histograms have NO gaps (continuous data) — gaps indicate discrete data (bar chart)
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Practice Questions for Histograms
A histogram shows the heights (cm) of plants in a garden with the following frequency densities: - 0 =< h < 5: frequency density = 4 - 5 =< h < 15: frequency density = 3 - 15 =< h < 25: frequency density = 6 - 25 =< h < 40: frequency density = 2 What is the modal class?
A histogram is drawn with unequal class widths. A student says: 'I can just use frequency on the y-axis instead of frequency density — the shape of the histogram will look the same.' Is the student correct? Explain your answer.
Quick Recall Flashcards
14 questions on Histograms — practise free
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