Comparing two sets of data using a measure of spread
It may also be necessary to compare two sets of data using a measure of central tendency whilst considering the A measure of spread found by subtracting the smallest number from the biggest number. In other words, the difference between the highest and lowest values in a set of data. of the data, which indicates the measure of spread.
Question
Alastair and Julie are comparing their results on the modular Science exams.
Using the mean and range, compare their performance.
Alastair:
\(Mean~=~\frac {32~+~56~+~40~+~38~+~52} {5}~=~\frac {218} {5}~=~43.6\)
\(Range~=~{56}~-~{32}~=~{24}\)
Julie:
\(Mean~=~\frac {39~+~43~+~47~+~40~+~49} {5}~=~\frac {218} {5}~=~43.6\)
\(Range~=~{49}~-~{39}~=~{10}\)
Alastair and Julie both scored a mean of 43.6 marks. Julie’s marks had a range of 10 compared to Alastair’s of 24 which means that her marks were much more consistent and closer together.
Whilst Alastair performed very well in unit 2, this is balanced by his poor performance in unit 1.
To summarise: the mean and range would suggest that Julie has performed better overall.
Question
Two pupils are in training for a 100m 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
Using the median and range, compare these two sets of data.
Although the medians suggest that pupil A is slightly quicker as their median is lower, their range is far larger than pupil B’s range. As pupil A’s times varied by a large amount (17 seconds between their fastest and slowest times) it suggests that pupil B is a better sprinter as their times are much more consistent, with the quickest and slowest times only differing by 5 seconds.
