A scatter graph is a statistical diagram drawn to compare two sets of data. It can be used to look for connections or a correlation between the two sets of data.
Example
A class took two tests. Test A was given early in the course and test B towards the end. The comparative results of these tests are given in the scatter graph below.
Each symbol on the graph shows the scores achieved in both tests by each of the pupils. So, for example, pupil A scored 60% on test A but only 20% on test B.
Pupil C achieved the top mark in test A.
Pupil P achieved the top mark in test B.
Pupil marked D came second in both tests.
Making comparisons
To find out whether the pupils generally did better in one test or the other, use a ruler or straight edge to draw a line joining marks that are the same on both tests, eg. 0 for both, 50 for both, 70 for both, etc.
The two students above the line achieved higher marks on test B than in test A.
The eight students below the line achieved higher marks on test A than on test B.
An important use of scatter graphs is to show how one set of results relates to another.
If the points on a scatter graph appear to be randomly scattered (see figure (i) below) there is unlikely to be any correlation between the two sets of data being measured.
If they form a more regular pattern (as in figure (ii) or figure (iii)), there is likely to be a correlation between them.
The scatter graph for the results from test A and test B, discussed earlier, is similar to figure (ii) and shows a correlation.
This suggests that test A and test B have a correlation because the pupils performed similarly in both tests. So the tests are likely to be based on the same subject or related subjects and set at a similar level.
The scatter graph enables one to identify particular pupils for whom action might be needed. For example, the reason why C achieved a high mark in test A but a low mark in test B might be investigated.
Worked examples
Example one
The scatter graph below compares the reading age and the actual age of a group of pupils.
How many pupils have a reading age below their actual age?
To find the answer to this question, it is helpful to draw a line (as shown) through any pair of points that represent the same ages on both scales.
For example, (5-10, 5-10) and (6-8, 6-8) or (7-4, 7-4), etc.
The five pupils whose marks are circled have a reading age that is clearly below their actual age.
How old is the pupil who has a reading age the same as their actual age?
To find the answer to this question, look at the line you have drawn, joining (5-10, 5-10) and (7-4, 7-4) and find the symbol which lies on it.
The pupil is aged 6 years and 1 month.
Example two
The PE department has been asked to show whether students in year 8 who do well in sporting activities do equally well in the sports theory part of the course and vice versa.
The students with the higher sporting activity results tend to get higher sports theory results. Those with the top two sporting activity marks indicated by circles also are among the top four theory results.
However, one student, M, achieved quite a high sporting activity result but came seventh out of 10 in sports theory. Conversely, J achieved quite a high mark in sports theory but the lowest mark in sporting activity.
Avoiding common errors
Most common errors can be avoided by:
- using a ruler or straight edge to move across the graph to help locate clusters of points
- drawing horizontal, vertical or 45 degree lines to break up the graph to allow groups of points to be located more easily, and
- remembering that each point represents one person.