Theory question 113
StatisticsThe table gives the distribution of marks of 60 candidates in a test.
Marks: 23−25, 26−28, 29−31, 32−34, 35−37, 38−40
frequency: 3, 7, 15, 21, 10, 4
(a) Draw a cumulative frequency curve of the distribution.
(b) From your curve, estimate the (i) 80th percentile; (ii) median (iii) semi-interquartile range.
Show the model answer
Model answer
(a) Upper class boundaries 25.5, 28.5, 31.5, 34.5, 37.5, 40.5 with cumulative frequencies 3, 10, 25, 46, 56, 60; plot and join with a smooth curve
(b)(i) 80th percentile = 48th mark ≈ 34.5 + (2/10) × 3 ≈ 35.1
(ii) Median = 30th mark ≈ 31.5 + (5/21) × 3 ≈ 32.2
(iii) Q1 = 15th mark ≈ 29.5, Q3 = 45th mark ≈ 34.4; semi-interquartile range ≈ (34.4 − 29.5)/2 ≈ 2.4 (accept readings from the curve)
Explanation
Plot cumulative frequency against upper class boundaries.