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WAEC 2019 · Paper 2 · Q6

Mass (kg) 10.5–14.4 14.5–24.4 24.5–44.4 44.5–47.4 47.5–49.4
Number of persons 2 6 18 2 1

The distribution of the masses of a group of persons is shown in the table.

  1. (a)

    Draw a histogram for the distribution.

    Model answer
    0.20.40.60.8Mass (kg)Frequency density10.4514.4524.4544.4547.4549.45

    The class widths are unequal (4, 10, 20, 3, 2), so the bar heights are frequency densities: 0.5,0.6,0.9,0.67,0.50.5, 0.6, 0.9, 0.67, 0.5. The bars stand on the class boundaries 10.45,14.45,24.45,44.45,47.45,49.4510.45, 14.45, 24.45, 44.45, 47.45, 49.45 and touch; the tallest bar is over 24.45–44.45.

Try it on a graph

Histogram with unequal widths: heights are frequency densities.

Worked solution (try it first)
  1. The class widths are unequal: 4,10,20,3,24, 10, 20, 3, 2 (from the boundaries).
  2. Frequency densities: 24=0.5\frac24 = 0.5, 610=0.6\frac{6}{10} = 0.6, 1820=0.9\frac{18}{20} = 0.9, 23≈0.67\frac23 \approx 0.67, 12=0.5\frac12 = 0.5.
  3. Draw each bar over its class boundaries with these heights, so that each bar's area is its frequency.

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