Theory question 105
StatisticsThe table shows the distribution of marks scored by 64 students in a test.
Marks: 10−19, 20−29, 30−39, 40−49, 50−59, 60−69, 70−79, 80−89, 90−99
Frequency: 2, 2, 2, 8, 13, 11, 12, 10, 4
(a) Draw a histogram for the distribution. (b) Use the histogram to estimate the modal score.
Show the model answer
Model answer
(a) Class boundaries 9.5, 19.5, …, 99.5 (equal widths of 10); bar heights are the frequencies. Label axes and give a scale.
(b) Tallest bar 49.5–59.5 (13). Join its top corners to the tops of the neighbouring bars (8 and 11) and read where the lines cross: mode ≈ 49.5 + 10 × 5/(5 + 2) ≈ 56.6, about 57.
Explanation
The crossing lines on the tallest bar locate the mode.