Introduction
Raw statistical data — an unorganised collection of values — must be presented in a clear, informative way before it can be interpreted. In the 9709 examination, you are expected to select an appropriate diagram for a given data set and articulate why that choice is (or is not) suitable. Questions often ask you to "state one advantage" or "give a reason why [diagram X] would not be appropriate", so understanding the strengths and weaknesses of each representation is just as important as knowing how to draw one.
Core Concept
Different diagrams suit different types and structures of data. The key questions to ask when choosing a representation are:
- Is the data quantitative (numerical) or qualitative (categorical)?
- Is the quantitative data discrete or continuous?
- Is the focus on distribution shape, spread, individual values, or comparison between groups?
- How many data points are there? (Stem-and-leaf is impractical for very large data sets, for example.)
The table below summarises the main representations in 9709 PS1 and the data type each suits.
| Diagram | Best suited to | Key feature |
|---|---|---|
| Stem-and-leaf diagram | Small/medium discrete or continuous data | Retains raw values; easy to find median/quartiles |
| Back-to-back stem-and-leaf | Comparing two small/medium data sets | Side-by-side comparison of two distributions |
| Box-and-whisker plot | Continuous (or discrete) data; comparison | Shows five-number summary; highlights outliers |
| Histogram | Continuous grouped data (unequal or equal class widths) | Area ∝ frequency; frequency density on -axis |
| Frequency diagram (bar chart for grouped) | Continuous grouped data with equal class widths | Height ∝ frequency when widths are equal |
| Bar chart | Discrete or qualitative data | Gaps between bars; height = frequency |
| Pie chart | Qualitative or discrete data; proportions | Angle ∝ relative frequency |
| Cumulative frequency graph (ogive) | Continuous grouped data | Estimates median, quartiles, percentiles |
| Dot plot / frequency table | Very small discrete data sets | Simple; shows every value |
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