Theory question 111
Data PresentationThe frequency distribution table shows the marks obtained by 100 students in a Mathematics test.
Marks (%): 1-10, 11-20, 21-30, 31-40, 41-50, 51-60, 61-70, 71-80, 81-90, 91-100
Frequency: 2, 3, 5, 13, 19, 31, 13, 9, 4, 1
(a) Draw a cumulative frequency curve for the distribution. (b) Use the graph to find the: (i) 60th percentile; (ii) probability that a student passed the test if the pass mark was fixed at 35%.
Show the model answer
(a) Upper boundaries 10.5, 20.5, …, 100.5 with cumulative frequencies 2, 5, 10, 23, 42, 73, 86, 95, 99, 100; plot and draw a smooth S-curve.
(b)(i) 60th student: about 50.5 + (60 − 42)/31 × 10 ≈ 56.3 marks.
(ii) Reading at 35: about 16 students scored below 35, so about 84 passed. Probability ≈ 84/100 = 0.84.
(Accept readings close to these from the curve.)
Plot each cumulative frequency at the upper class boundary.