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Nov 2013 p63 q1
2401
The distance of a student’s home from college, correct to the nearest kilometre, was recorded for each of 55 students. The distances are summarised in the following table.
Distance from college (km)
1–3
4–5
6–8
9–11
12–16
Number of students
18
13
8
12
4
Dominic is asked to draw a histogram to illustrate the data. Dominic’s diagram is shown below.
Give two reasons why this is not a correct histogram.
Solution
1. In a correct histogram, the bars should be adjacent to each other without gaps, as the data is continuous. The diagram shows gaps between the bars, which is incorrect.
2. In a histogram, the area of each bar should represent the frequency of the data. This requires using frequency density, calculated as \(\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}}\). The diagram does not use frequency density, leading to incorrect bar heights.