3.1 Scatter graphs
A scatter graph is a way to present bivariate data so you can see more easily if there is a relationship between the two data variables. Alternative expressions for scatter graph are scattergram, scatterplot and scatter diagram.
ACTIVITY 6
Here is a graph showing some pupils’ handspans and heights. Each cross plotted on the graph represents a pupil.
Figure 12 A coordinate grid showing five sets of bivariate data plotted- Plot the data for the following three pupils on the graph
| Pupil | Handspan (cm) | Height (cm) |
| 1 | ||
| 2 | ||
| 3 |
- From the graph, can you say anything about a potential relationship between a pupil’s handspan and height?
- Measure your own handspan and height in centimetres. Think about how this fits with the existing data shown.
Comment
- The completed graph should look like this (pupils added shown in orange):
- There appear to be two small clusters of data, five pupils with smaller handspans who have shorter heights and three pupils with larger handspans who are taller. So, this may suggest there is a possible relationship between handspan and height of pupils.
- Your own data may fit within any pattern you identified, but equally, it may not! We are all unique individuals. Often patterns in measurement data for human characteristics such as handspan and height are slightly less apparent for children’s datasets compared to adult datasets due to adolescent growth spurts and the fact that children are not yet fully grown.
In the last activity the points on the graph were plotted using crosses rather than dots or another symbol. Using crosses means the specific coordinate can be indicated clearly; learners sometimes use ‘blobs’ which can have quite large error margins thereby not giving a clear picture of the data plotted. The more data you have, the easier it can be to identify a potential relationship, but also, the ‘busier’ your graph will become. Before you look at how you identify a potential relationship, try the following activity.
ACTIVITY 7
Below are some scatter graphs. Drag and drop each image under the appropriate heading according to whether you think the variables represented by the points plotted on the graph are related.
comment from Ana; this might become h5p activityComment
Scatter graph 1 could be argued either way. You may see a loose (weak) relationship that follows an approximate downward trend from the top left of the plot area to the bottom right. Or you might just think the points are fairly scattered across the plot area.
Scatter graph 2 seems to show a strong relationship between variable A and B since the points are tightly grouped together around an invisible line with increasing gradient.
Scatter graph 3 does not seem to show a relationship between variable A and B since the points are well scattered over most of the plot area.
Scatter graph 4 could be argued either way. You may see a loose (weak) relationship that follows an approximate upward trend from the bottom left of the plot area to the top right. Or you might just think the points are fairly scattered across the plot area.
In the previous activity you saw some examples of scatter graphs where one variable is on the horizontal axis and the other is on the vertical axis. If the points seem to follow a pattern it could be said there is a relationship between the two variables. Here is scatter graph 2 again, with the variable names added.
Figure 14 A scatter graph showing monthly minimum and maximum temperatures for Stornoway, 2023Source: Historic station data - Met OfficeThis scatter graph was created using some of the weather data that you looked at in Week 5. It shows the maximum monthly temperature plotted against the minimum monthly temperature for Stornoway. You would perhaps expect a link between these two pieces of information given that, as the seasons change in the UK, the whole range of temperatures changes accordingly, see Figure 15.
Figure 15 A dual line graph showing the monthly temperature average in Stornoway, 2023As you can see from the line graph above, the trend for both minimum and maximum temperature over the year is very similar. Therefore, as one temperature increases, so does the other and vice versa, though the two graphs are not perfectly parallel.