EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
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Statistics & Probability · Higher

Histograms

Histograms display continuous data in classes. Unlike bar charts, the area of each bar represents frequency, not the height. The y-axis shows frequency density.

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Key facts to remember

  • 1Frequency density = frequency ÷ class width.
  • 2Frequency = frequency density × class width (area of bar).
  • 3There are no gaps between bars in a histogram.
  • 4Classes do not need to be equal width.
  • 5The y-axis is always labelled "frequency density", not "frequency".
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Formulas

Frequency density
FD = Frequency ÷ Class width
Frequency
Frequency = FD × Class width
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Worked examples

Example 1

A class 20 ≤ t < 30 has frequency 40. Calculate the frequency density.

Working

  1. Class width = 30 − 20 = 10
  2. Frequency density = 40 ÷ 10 = 4
AnswerFrequency density = 4
Example 2

A bar on a histogram has frequency density 3 and class width 5. Find the frequency.

Working

  1. Frequency = FD × class width = 3 × 5 = 15
AnswerFrequency = 15
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Common mistakes

✗Reading the height of the bar as the frequency instead of using frequency density × class width.
✗Leaving gaps between bars (histograms show continuous data — no gaps).
✗Forgetting to label the y-axis as frequency density.
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Exam tips

✓Always add a "class width" and "FD" column to your table before drawing a histogram.
✓To find frequency from a histogram: frequency = height × width (area of bar).

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