Theory question 109
Data PresentationThe marks obtained by 40 students in an examination are as follows:
85 77 87 74 77 78 79 89 85 90
78 73 86 83 91 74 84 81 83 75
77 70 81 69 75 63 76 87 61 78
69 96 65 80 84 80 77 74 88 72
(a) Copy and complete the table for the distribution using the above data.
Class Boundaries: 59.5 – 64.5, 64.5 – 69.5, 69.5 – 74.5, 74.5 – 79.5, 79.5 – 84.5, 84.5 – 89.5, 89.5 – 94.5, 94.5 – 99.5 (with Tally and Frequency columns)
(b) Draw a histogram to represent the distribution (c) Using your histogram, estimate the modal mark (d) If a student is chosen at random, find the probability that the student obtains a mark greater than 79.
Show the model answer
(a) Frequencies: 59.5–64.5: 2; 64.5–69.5: 3; 69.5–74.5: 6; 74.5–79.5: 11; 79.5–84.5: 8; 84.5–89.5: 7; 89.5–94.5: 2; 94.5–99.5: 1 (total 40).
(b) Bars on the class boundaries with heights equal to the frequencies.
(c) In the tallest bar (74.5–79.5) join its top corners to the tops of the next bars; the lines cross at about 77.6, so the modal mark ≈ 78.
(d) Marks above 79: 8 + 7 + 2 + 1 = 18, so P = 18/40 = 9/20.
Tally the marks one by one and check the frequencies add up to 40.