Theory question 107
Data PresentationThe data show the marks obtained by students in a Biology test.
52 56 25 56 68 73 66 64 56 48
20 39 9 50 46 54 54 40 50 96
36 44 18 97 65 21 60 44 54 32
92 49 37 94 72 88 89 35 59 34
15 88 53 16 84 52 72 46 60 42
(a) Construct a frequency distribution table using the class interval 0 − 9, 10 − 19, 20 − 29, …
(b) Draw a cumulative frequency curve for the distribution.
(c) Use the graph to estimate the: (i) median; (ii) percentage of students who scored at least 66 marks, correct to the nearest whole number.
Show the model answer
(a) Frequencies: 0–9: 1; 10–19: 3; 20–29: 3; 30–39: 6; 40–49: 8; 50–59: 12; 60–69: 6; 70–79: 3; 80–89: 4; 90–99: 4 (total 50)
Cumulative: 1, 4, 7, 13, 21, 33, 39, 42, 46, 50
(b) Plot cumulative frequency against upper class boundaries 9.5, 19.5, …, 99.5 and join with a smooth S-shaped curve
(c)(i) Median at the 25th student: about 53 (calculation gives 49.5 + 4/12 × 10 ≈ 52.8)
(ii) About 37 students scored below 65.5, so about 13 scored at least 66
Percentage ≈ 13/50 × 100 ≈ 27% (accept 26–28% from the graph)
Plot at the upper class boundaries, not the class limits.