Theory question 114
StatisticsThe following table shows the distribution of marks obtained by some students in an examination.
Marks: 0 − 9, 10 − 19, 20 − 29, 30 − 39, 40 − 49, 50 − 59, 60 − 69, 70 − 79, 80 − 89, 90 − 99
No. of students: 50, 50, 40, 60, 100, 100, 50, 25, 15, 10
(a) Construct a cumulative frequency table for the distribution. (b) Draw an ogive for the distribution. (c) Use your graph in (b) to determine the (i) semi-interquartile range; (ii) number of students who failed, if the pass mark for the examination is 37; (iii) probability that a student selected at random scored between 20% and 60%.
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(a) Cumulative frequencies: 50, 100, 140, 200, 300, 400, 450, 475, 490, 500
(b) Plot cumulative frequency against upper class boundaries 9.5, 19.5, …, 99.5 and join with a smooth curve
(c)(i) Q1 (125th) ≈ 25.8, Q3 (375th) ≈ 57; semi-interquartile range ≈ (57 − 25.8)/2 ≈ 15.6 (about 15–16 from the graph)
(ii) Reading at 36.5: about 182 students failed (about 180)
(iii) (400 − 100)/500 = 3/5
Read quartiles at the 125th and 375th positions of 500 on the ogive.