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WAEC 2009 · Paper 2 · Q7

The marks scored by 50 students in a Geography examination are as follows:
60 54 40 67 53 73 37 55 62 43
44 69 39 32 45 58 48 67 39 51
46 59 40 52 61 48 23 60 59 47
65 58 74 47 40 59 68 51 50 50
71 51 26 36 38 70 46 40 51 42
  1. (a)

    Using class intervals 21 – 30, 31 – 40, …, prepare a frequency distribution table.

    Model answer
    Marks 21–30 31–40 41–50 51–60 61–70 71–80
    Class boundaries 20.5–30.5 30.5–40.5 40.5–50.5 50.5–60.5 60.5–70.5 70.5–80.5
    Frequency 2 10 12 15 8 3
  2. (b)

    Draw a histogram to represent the distribution.

    Model answer
    20.530.540.550.560.570.580.5246810121416MarksFrequency53.5

    Use the class boundaries 20.5, 30.5, …, 80.5 on the horizontal axis and draw bars with no gaps, of heights 2, 10, 12, 15, 8 and 3.

  3. (c)

    Use your histogram to estimate the modal mark.

  4. (d)

    If a student is selected at random, find the probability that he or she obtains a mark greater than 63.

Worked solution (try it first)

(a)

  1. Tally the marks into the classes: the frequencies are 2, 10, 12, 15, 8 and 3 (total 50).

(b)

  1. Draw the bars on the class boundaries 20.5,30.5,…,80.520.5, 30.5, \dots, 80.5, touching each other, with heights equal to the frequencies.

(c)

  1. On the tallest bar (50.5–60.5), join its top-left corner to the top of the next bar (height 8) and its top-right corner to the top of the previous bar (height 12).
  2. Read the mark where the lines cross: about 50.5+15−12(15−12)+(15−8)×10=53.550.5 + \frac{15 - 12}{(15 - 12) + (15 - 8)} \times 10 = 53.5.

(d)

  1. Count the marks greater than 63 in the list: 67, 73, 69, 67, 65, 74, 68, 71 and 70, which is 9 students.
  2. Probability =950=0.18= \frac{9}{50} = 0.18.

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