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Histograms Cambridge IGCSE Mathematics (9–1) revision

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In plain words

A histogram looks like a bar chart, but there's a difference that matters: it's the area of each bar, not its height, that shows the frequency. That lets it handle groups of different widths fairly.

Three things to know

  1. The height of each bar is the frequency density: frequency ÷ class width.
  2. So frequency = frequency density × class width, which is the area of the bar.
  3. With equal class widths a histogram looks like a bar chart with no gaps. With unequal widths, always work with areas.

Worked example

A class from 10 to 30 has a frequency of 40. Find the frequency density.

  1. Class width = 30 − 10 = 20.
  2. Frequency density = frequency ÷ class width = 40 ÷ 20.
  3. = 2.

Tips and tricks

  • The vertical axis is frequency density, not frequency. Label it.
  • To read a frequency off a histogram, multiply the height of the bar by its width.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Histograms: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. What does the area of a bar on a histogram show?
    • the class width
    • the frequency (the answer)
    • the frequency density
    • the mean

    Area = frequency density × class width.

  2. How is frequency density calculated?
    • frequency × class width
    • frequency ÷ class width (the answer)
    • class width ÷ frequency
    • frequency + class width

    It is the height of the bar.

  3. A class has width 10 and frequency 50. What is its frequency density?
    • 500
    • 60
    • 5 (the answer)
    • 0.2

    50 ÷ 10.

  4. A bar has width 5 and height 4. What frequency does it show?
    • 9
    • 1.25
    • 20 (the answer)
    • 0.8

    5 × 4.

  5. What goes on the vertical axis of a histogram?
    • frequency
    • frequency density (the answer)
    • class width
    • cumulative frequency

    That is what makes unequal class widths fair.

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