The marks of the pupils in a certain class in a History examination are as follows.
28, 33, 55, 38, 42, 39, 27, 48, 51, 37, 57, 49, 33
The marks of the pupils in a Physics examination are summarised as follows.
Lower quartile: 28, Median: 39, Upper quartile: 67. The lowest mark was 17 and the highest mark was 74.
- Draw box-and-whisker plots in a single diagram on graph paper to illustrate the marks for History and Physics.
- State one difference, which can be seen from the diagram, between the marks for History and Physics.
Solution
To draw the box-and-whisker plots:
History:
- Order the marks: 27, 28, 33, 33, 37, 38, 39, 42, 48, 49, 51, 55, 57
- Lowest mark: 27
- Highest mark: 57
- Median: 39 (7th value)
- Lower quartile (LQ): 33 (average of 3rd and 4th values)
- Upper quartile (UQ): 50 (average of 10th and 11th values)
Physics:
- Lowest mark: 17
- Highest mark: 74
- Lower quartile (LQ): 28
- Median: 39
- Upper quartile (UQ): 67
Draw the box-and-whisker plots on a uniform scale with appropriate labels.
Difference: The Physics marks are more spread out than the History marks, as indicated by the wider range and interquartile range in the Physics data.
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