Graphs and Charts
Section: Statistics | Syllabus: Cambridge Primary Mathematics (0845)
Choosing How to Represent Data
Different types of data are best shown using different representations. Choosing the right one - and being able to explain why - is as important as knowing how to draw it.
- Venn diagrams and Carroll diagrams sort data into overlapping or non-overlapping categories
- Tally charts and frequency tables count how often each value or category occurs
- Bar charts compare frequencies across separate categories
- Waffle diagrams and pie charts show how a whole splits into proportional parts
- Frequency diagrams show grouped continuous data, such as height ranges, with no gaps between the bars
- Line graphs show how a value changes over time
- Scatter graphs show the relationship between two different variables
- Dot plots show individual values along a number line, useful for spotting clusters
| Representation | Best used for |
|---|---|
| Venn diagram | Sorting data by whether it belongs to one, both, or neither of two categories |
| Carroll diagram | Sorting data using two yes/no criteria in a grid |
| Tally chart / frequency table | Counting occurrences of each value or category |
| Bar chart | Comparing frequencies across separate categories |
| Waffle diagram / pie chart | Showing how a whole splits into proportional parts |
| Frequency diagram | Showing grouped continuous data, with no gaps between bars |
| Line graph | Showing how a value changes over time |
| Scatter graph | Showing the relationship between two variables |
| Dot plot | Showing individual values along a number line to spot clusters |
A waffle diagram and a pie chart can show the same proportion of a whole in different visual forms
A scatter graph compares two variables; a dot plot shows how single values cluster along one number line
Worked Example: Choosing the Best Representation
- Question: A class collected data on each student's exact arm span in cm. Which representation would best show this data, and why?
- Step 1: Arm span in cm is continuous data - it can take any value, not just whole numbers
- Step 2: Continuous data grouped into ranges is best shown with a frequency diagram, since its bars have no gaps
- Answer: A frequency diagram, grouping arm spans into ranges such as 120-129 cm and 130-139 cm
Common Mistakes
MistakeUsing a pie chart for data that changes over time
Fixa pie chart shows how a whole splits into parts at one moment - to show a value changing over time, use a line graph instead
MistakeConfusing a bar chart with a frequency diagram
Fixthe gaps matter - bars touch for continuous grouped data (a frequency diagram) but stay separated for categories that don't run into each other (a bar chart)
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