Theory question 110
Data PresentationThe table shows the distribution of marks obtained by 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
Frequency: 7, 11, 17, 20, 29, 34, 30, 25, 21, 6
(a) Construct a cumulative frequency table for the distribution.
(b) Draw the cumulative frequency curve for the distribution.
(c) Using the curve, find correct to one decimal place, the: (i) median mark; (ii) lowest mark for distinction if 5% of the students passed with distinction.
Show the model answer
(a) Upper class boundaries 9.5, 19.5, …, 99.5; cumulative frequencies 7, 18, 35, 55, 84, 118, 148, 173, 194, 200
(b) Plot cumulative frequency against upper class boundary and draw a smooth S-curve
(c)(i) Median at the 100th student: ≈ 54.2 (49.5 + 16/34 × 10)
(ii) Top 5% = 10 students, so read the mark at cumulative frequency 190: ≈ 87.6 (79.5 + 17/21 × 10)
For the distinction mark, count down from the top: 200 − 10 = 190.