Statistics
Tables & Charts: Bar Charts, Pie Charts, and Scatter Graphs
Year 7 · Year 8 · Year 9
- ✓By the end of this lesson students will be able to construct and interpret bar charts for discrete data.
- ✓By the end of this lesson students will be able to construct and interpret pie charts to show proportions.
- ✓By the end of this lesson students will be able to plot and interpret scatter graphs.
- ✓By the end of this lesson students will be able to describe and identify different types of correlation from scatter graphs.
Key concepts
A bar chart is used to display discrete data (data that can only take specific values, often categories). It uses bars of equal width, with gaps between them, to represent the frequency or count of each category. The height of each bar is proportional to the frequency it represents. Bar charts are excellent for comparing quantities across different categories.
A pie chart is a circular chart divided into sectors, where each sector represents a proportion of the whole. The area of each sector (and thus its angle at the centre) is proportional to the frequency or value it represents. Pie charts are useful for showing how a whole is divided into parts and are best used when there are not too many categories.
A scatter graph (or scatter plot) is used to display the relationship between two numerical variables. Each point on the graph represents a pair of data values. One variable is plotted on the x-axis and the other on the y-axis. Scatter graphs help us to see if there is a pattern or trend between the two variables, known as correlation.
Correlation describes the strength and direction of a relationship between two variables shown on a scatter graph. - **Positive correlation**: As one variable increases, the other variable also tends to increase. The points generally go upwards from left to right. - **Negative correlation**: As one variable increases, the other variable tends to decrease. The points generally go downwards from left to right. - **No correlation**: There is no clear relationship or pattern between the two variables. The points are scattered randomly. - A **line of best fit** (or trend line) can be drawn on a scatter graph to show the general trend of the data. It should have roughly the same number of points above and below it.
Key facts to remember
- 1Bar charts use bars of equal width with gaps to represent discrete data.
- 2The height of a bar in a bar chart indicates its frequency.
- 3Pie charts show proportions of a whole, with the angle of each sector proportional to its frequency.
- 4The sum of all angles in a pie chart must be 360°.
- 5Scatter graphs show the relationship between two numerical variables.
- 6Positive correlation means as one variable increases, the other tends to increase.
- 7Negative correlation means as one variable increases, the other tends to decrease.
- 8No correlation means there is no clear relationship between the variables.
- 9A line of best fit can be drawn on a scatter graph to show the general trend of the data.
Worked examples
Example 1
The table shows the favourite colours of 30 students. Construct a bar chart to represent this data. | Colour | Frequency | | :----- | :-------- | | Red | 8 | | Blue | 10 | | Green | 5 | | Yellow | 3 | | Purple | 4 |
Answer
A bar chart with 'Colour' on the x-axis and 'Frequency' on the y-axis, with bars of heights 8 (Red), 10 (Blue), 5 (Green), 3 (Yellow), and 4 (Purple), all of equal width and with equal gaps between them.
Remember to always label your axes and give your chart a clear title.
Example 2
A survey of 60 people asked about their favourite type of film. The results are shown in the table. Construct a pie chart to represent this data. | Film Type | Frequency | | :-------- | :-------- | | Action | 20 | | Comedy | 15 | | Drama | 10 | | Sci-Fi | 15 |
Answer
A pie chart with sectors of 120° (Action), 90° (Comedy), 60° (Drama), and 90° (Sci-Fi), each clearly labelled.
Accuracy with a protractor is key for drawing pie charts correctly.
Example 3
The table shows the number of hours spent revising and the test score for 8 students. Plot this data on a scatter graph and describe the correlation. | Hours Revised | Test Score (%) | | :------------ | :------------- | | 2 | 45 | | 3 | 50 | | 5 | 70 | | 1 | 30 | | 4 | 60 | | 6 | 85 | | 3 | 55 | | 5 | 75 |
Answer
A scatter graph with points plotted at (2,45), (3,50), (5,70), (1,30), (4,60), (6,85), (3,55), (5,75). The points show a general upward trend from left to right, indicating a positive correlation.
When describing correlation, state both the direction (positive/negative) and the strength (strong/weak, though 'strong' and 'weak' are more advanced for KS3, 'general trend' is sufficient).
Common mistakes
- ✗Forgetting to label axes or give a title to charts.
- ✗Using unequal widths for bars in a bar chart, or having no gaps for discrete data.
- ✗Incorrectly calculating angles for pie charts, or not ensuring they sum to 360°.
- ✗Plotting points inaccurately on scatter graphs.
- ✗Confusing positive and negative correlation, or describing a trend when there is none.
Exam tips
- ★Always use a ruler and pencil for drawing all charts and graphs.
- ★For pie charts, show your angle calculations clearly as working out marks are often awarded.
- ★When plotting scatter graphs, ensure your scales are consistent and cover the full range of your data.
- ★Practice describing correlation using clear language, referring to both variables in your explanation.
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