Theory question 112
Data PresentationThe table below shows the mark distribution of candidates in an aptitude test for selection into the public service.
Mark (in %): 44–46, 47–49, 50–52, 53–55, 56–58, 59–61, 62–64, 65–67, 68–70, 71–73
Frequency: 2, 5, 11, 20, 26, 42, 46, 36, 9, 3
(a) Make a cumulative frequency for the distribution.
(b) Draw the cumulative frequency curve.
(c) From your graph estimate the median mark.
(d) The cut-off mark was 63%. What percentage of the candidates was selected?
Show the model answer
(a) Upper class boundaries 46.5, 49.5, 52.5, 55.5, 58.5, 61.5, 64.5, 67.5, 70.5, 73.5 with cumulative frequencies 2, 7, 18, 38, 64, 106, 152, 188, 197, 200.
(b) Plot cumulative frequency against upper class boundary (start at (43.5, 0)) and join with a smooth S-shaped curve.
(c) Median at the 100th candidate: 58.5 + (100 − 64)/42 × 3 ≈ 61% (from the graph about 61).
(d) Candidates below 62.5: about 106 + 46/3 ≈ 121, so about 79 scored 63 or more: 79/200 × 100 ≈ 39% (accept 36–40% read from the graph).
Always plot cumulative frequency against the upper class boundary, not the class mark.