If you work through this section you should be able to:
This section requires some understanding of different kinds of chart and how they can be used effectively (see Introduction to charts section).
You may also find the Processing and representing data using charts section useful.
Where a table with columns and rows simply presents raw data, a chart highlights the trends and changes in data series and the relationships between different sets of data.
Have a go at the activities that follow before going on to the explanations. This will give you a chance to question and analyse what you see.
Have a look at the following pie chart showing the crops of a farm of 200 square kilometres:
If we already know that the total is 200 square km, estimate the values for the crops. You can either write these down on a piece of paper or print off this page and fill them in. The values for grass have already been given.
| Crops | Fraction | Percentage | Actual square kilometres |
|---|---|---|---|
| Oats | |||
| Grass | 1/4 | 25% |
50 |
| Barley | |||
| Wheat |
Here is the completed pie chart for Activity 1:
Here is the completed data table:
| Crops | Fraction | Percentage | Actual square kilometres |
|---|---|---|---|
| Oats | 1/8 | 12.5% | 25 |
| Grass | 1/4 | 25% |
50 |
| Barley | 3/8 | 37.5% | 75 |
| Wheat | 1/4 | 25% |
50 |
Pie charts highlight the proportions of values in relation to the whole.
The wheat section represents around a quarter (1/4) of the whole circle. This is equal to 25%. 25% of 200 square km is 50.
The oats section is around a half the size of the grass and wheat sections. Therefore, it is 1/8, or 12.5% and equal to 25 square km.
The barley section can be worked out by adding up the values of the other sections and taking this away from the total (200 square km). The value is 75, which is 37.5% of the total (200 square km). This is equal to 3/8.
To interpret data from pie charts it is important to have some understanding of fractions and percentages. You can see the relevant themes on this site for guidance on these.
This activity has asked you to think about the detail (the values) that a chart represents. In the following activities you will look more at the overall relationships being illustrated.
In an opinion poll, 500 people were asked whether they agreed with the opinion of an MP. Look at the following chart and on a piece of paper describe the changes that are being shown over the three months. Look at the relationships between data series, as well as the detailed figures for each series.
You may have noted the following:
Look at each data series separately - it is easy to do this when they have different colours or patterns to distinguish them. You can then see clearly how each separate data series change over time.
Also look closely at the three different data series for each month. In May the difference between 'yes's and 'no's and 'undecided's is much less than in March.
Charts illustrate relationships between data series, so interpreting charts involves identifying these different relationships and then scrutinising any changes and comparisons. You may also need to look more closely at the details, identifying figures and times from the horizontal and vertical axis to illustrate what you are saying about these relationships.
Interpreting data can go even further once we start to put it into context. If you had been told that bad publicity about the particular MP, and also about the view in question, had been rife throughout May, you could interpret more from the data - that media coverage affected the popularity of the MP and the particular view expressed.
Line charts (often referred to simply as 'graphs') can be more difficult to understand than pie or column charts and require more effort to interpret. However, the main trends are easily identifiable at a glance. Have a look at the following line chart and, on paper, write down answers to the questions that follow.
1. What is the graph comparing?
2. What is the trend for both companies in the latter part of 2008?
3. In which years did the two companies have the same profit?
4. How do the two companies' profits compare over the time period shown?
1. The graph is comparing the profits of Company X and Company Y over a period from June 2005 to December 2008.
2. Both companies' profits have fallen in the second half of 2008.
3. Between June and December of 2007 and between June and December of 2008 both companies had the same profit.
4. At the beginning and the end of the time period shown, Company Y has higher profits than X, and although profits rise and fall they do so more steadily, always staying between around £28,000 and £37,000. Company X starts and ends with lower profits than Y but does achieve the highest profit margin of the whole time period shown (£40,000 in June 2001). Company X's profits fluctuate more severely: over the time period shown they range from £10,000 to £40,000.
Look at where the peaks and troughs are and look at how the two lines compare to each other. The chart allows you to clearly see and compare where the profits of the two companies rise and fall and at which points of time they do this gradually or more quickly.
An important part of interpreting any information is understanding exactly what is being shown and what is not being shown. Always ask questions about the purpose and origins of data.
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