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WAEC 2011 · Paper 2 · Q7

A tyre manufacturing company researched into the life span of one type of their motorcycle tyres. The results were as follows:

Distance (1000 km) 10–19 20–29 30–39 40–49 50–59 60–69
Number of tyres 30 69 93 57 36 15
  1. (a)

    Draw a histogram for the distribution.

    Model answer
    9.519.529.539.549.559.569.520406080Distance (1000 km)Number of tyresmode ≈ 33.5

    Draw bars on the class boundaries, not the class limits (9.5, 19.5, …, 69.5), with no gaps between them. The height of each bar is the frequency, and each axis is labelled.

    To estimate the mode, take the tallest bar. Join its top-left corner to the top-left corner of the bar on its right, and its top-right corner to the top-right corner of the bar on its left. Read down from where the two lines cross: the mode is about 33.5 thousand km.

  2. (b)

    Use the histogram to estimate the mode.

Try it on a graph

Histogram on the class boundaries (1000 km). The red lines cross above the mode, about 33.5.

Worked solution (try it first)

(a)

  1. The classes have equal widths, so draw bars of heights 30,69,93,57,36,1530, 69, 93, 57, 36, 15 over the boundaries 9.5,19.5,…,69.59.5, 19.5, \ldots, 69.5.

(b)

  1. On the tallest bar (30–39), join each top corner to the top corner of the opposite neighbour.
  2. The lines cross over the mode.
  3. By calculation: 29.5+93−69(93−69)+(93−57)×10=29.5+2460×1029.5 + \dfrac{93 - 69}{(93 - 69) + (93 - 57)} \times 10 = 29.5 + \dfrac{24}{60} \times 10
    =33.5= 33.5 thousand km.

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