Theory question 113
Data PresentationThe table shows the distribution of marks of candidates.
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 and draw a cumulative frequency curve.
(b) Use the curve to estimate, correct to one decimal place, the: (i) lowest mark for distinction if 5 % of the candidates passed with distinction; (ii) probability of selecting a candidate who scored at most 45%.
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. Plot cumulative frequency against upper class boundary and join with a smooth S-shaped curve.
(b)(i) 5% of 200 = 10, so read the mark at cumulative frequency 190: ≈ 79.5 + (17/21) × 10 ≈ 87.6
(ii) At 45 marks the cumulative frequency ≈ 71, so probability ≈ 71/200 ≈ 0.36 (accept readings from the curve)
Plot against upper class boundaries, not class marks.