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Histograms

Statistics

From a table

  • Work out every frequency density before touching the graph
  • Draw each bar with its width along the horizontal axis and its height equal to the frequency density
  • The bars sit edge to edge with no gaps
  • Questions usually give a partly-drawn histogram and ask you to complete it, rather than starting from blank axes
  • Read the scale on the frequency density axis carefully, since one square is rarely one unit
A histogram of distances in metres drawn from a frequency table, its bars sitting edge to edge with no gaps: densities of 0.5 from 40 to 50, 2.4 from 50 to 55, 2.8 from 55 to 60, 2 from 70 to 75 and 0.8 from 75 to 80
Source: Drawing histograms by Save My Exams

When no frequency density scale is given

  • A variant gives the height of one bar in centimetres and asks for the heights of the others
  • Heights are proportional to frequency density, so find the scale from the bar you are given, then apply it
    • If a class with frequency density 3.5 is drawn 7 cm tall, then 1 unit of frequency density is 2 cm
    • A class with frequency density 1.2 is then drawn 2 × 1.2 = 2.4 cm tall
  • The method is identical; only the units on the vertical axis change