Comparing two sets of data
It may be useful to compare two sets of data using the mean, mode or median in order to draw conclusions about the information presented.
You may be choosing one measure over another for its accuracy or choosing the one that best backs up what you want to show.
Question
Robert and Emily are both preparing for their Mathematics GCSE. Their results on 10 practice papers are as follows:
Robert: 63, 86, 64, 67, 71, 42, 79, 64, 80, 64
Emily: 61, 73, 82, 90, 61, 67, 76, 40, 80, 62
- Using the mean, determine who is performing better in their Maths tests.
- Could Robert use the mean, mode or median to suggest that he is better at Maths than Emily?
Would this be a true representation of their results?
1. The mean suggests that Emily is performing better than Robert.
Robert’s mean = 68
Emily’s mean = 69.2
2. Emily’s mean is higher, suggesting she is better.
Emily’s median of 70 marks compared to Robert’s of 65.5 again suggests that Emily is better.
Robert’s mode is 64 which, when compared to Emily’s mode of 61 marks, could be used to evidence that Robert is better at maths.
This would be an unfair representation, even though Robert got a score of 64 more than once. As it only happened three times, the mode is not a reliable indicator of the rest of his results.
Question
Two pupils are in training for a 100 m sprint. Their test runs are as follows (all times are given in seconds):
Pupil A: 20, 19, 22, 18, 20, 21, 18, 35
Pupil B: 18, 19, 18, 21, 21, 21, 23, 22
Which measure of central tendency could each pupil use to prove they are the faster sprinter?
Pupil A could use either the median or mode and state that they are ‘on average’ 1 second faster than pupil B.
Pupil B could use the mean and state that they are ‘on average’ 1.25 seconds faster than pupil B.
