Theory question 112
Data PresentationThe frequency distribution of the weight of 100 participants in a high jump competition is as shown below:
Weight (kg): 20-29, 30-39, 40-49, 50-59, 60-69, 70-79
Number of participants: 10, 18, 22, 25, 16, 9
(a) Construct the cumulative frequency table.
(b) Draw the cumulative frequency curve.
(c) From the curve, estimate the: (i) median; (ii) semi-interquartile range; (iii) probability that a participant chosen at random weighs at least 60kg.
Show the model answer
(a) Upper class boundaries 29.5, 39.5, 49.5, 59.5, 69.5, 79.5 with cumulative frequencies 10, 28, 50, 75, 91, 100.
(b) Plot cumulative frequency against upper boundary and join with a smooth S-shaped curve.
(c)(i) Median (50th) ≈ 49.5 kg.
(ii) Q1 (25th) ≈ 37.8 kg, Q3 (75th) ≈ 59.5 kg; semi-interquartile range ≈ (59.5 − 37.8)/2 ≈ 10.8 kg.
(iii) At least 60 kg: 16 + 9 = 25 participants, probability = 25/100 = 1/4.
(Accept readings close to these from the curve.)
Plot cumulative frequencies at the upper class boundaries.