Statistics
Charts & Diagrams
Year 10 · Year 11
- ✓Construct and interpret bar charts for discrete data.
- ✓Construct and interpret pie charts to represent proportional data.
- ✓Construct and interpret stem-and-leaf diagrams, including back-to-back diagrams.
- ✓Construct and interpret time series graphs to show trends over time.
- ✓Critically evaluate and compare different types of charts and diagrams.
Key concepts
A bar chart is used to represent discrete data. Each bar represents a category, and its height (or length, if horizontal) shows the frequency or count for that category. There should be gaps between the bars to indicate that the data is discrete.
A pie chart is used to display parts of a whole, showing the proportion of each category relative to the total. The entire circle represents the total frequency (360°), and each sector's angle is proportional to the frequency of its category.
A stem-and-leaf diagram is a way of organising numerical data to show its distribution while retaining all the original data values. Each data value is split into a 'stem' (the leading digit(s)) and a 'leaf' (the trailing digit). Data in the 'leaf' column must be ordered, and a 'key' is essential to explain how to read the diagram.
A time series graph is used to plot data that changes over a period of time. Time is always plotted on the horizontal (x) axis, and the measured variable is plotted on the vertical (y) axis. The data points are then joined by straight lines to show trends or patterns over time.
Key facts to remember
- 1Bar charts are used for discrete data, with gaps between bars.
- 2Pie charts show proportions of a whole; the sum of angles must be 360°.
- 3Stem-and-leaf diagrams display numerical data, retaining original values, and require a key.
- 4Time series graphs plot data against time to show trends; time is always on the horizontal axis.
- 5All charts and diagrams must have clear titles and labelled axes (where applicable).
- 6Choose the appropriate chart type based on the type of data you are representing (e.g., discrete, continuous, categorical, time-dependent).
- 7Data in stem-and-leaf diagrams must be ordered in the 'leaf' column.
Worked examples
Example 1
A survey asked 80 students about their favourite type of film. The results were: Action: 30, Comedy: 20, Drama: 15, Sci-Fi: 10, Other: 5. Construct a pie chart to represent this data.
Answer
A pie chart with sectors: Action (135°), Comedy (90°), Drama (67.5°), Sci-Fi (45°), Other (22.5°), each labelled appropriately.
Always use a protractor and compass for accurate pie chart construction. Ensure all sectors are clearly labelled.
Example 2
The number of points scored by a basketball team in 18 matches were: 78, 85, 92, 71, 88, 75, 90, 81, 79, 83, 95, 77, 80, 86, 74, 91, 82, 76. Construct an ordered stem-and-leaf diagram for this data and find the median.
Answer
Stem-and-leaf diagram: 7 | 1 4 5 6 7 8 9 8 | 0 1 2 3 5 6 8 9 | 0 1 2 5 Key: 7 | 1 represents 71 points Median = 81.5 points.
Remember to always include a key for a stem-and-leaf diagram. The leaves must be ordered numerically.
Example 3
The average monthly rainfall (mm) in a town for the first 7 months of a year was: Jan: 60, Feb: 55, Mar: 65, Apr: 70, May: 60, Jun: 50, Jul: 45. Draw a time series graph and describe the trend in rainfall.
Answer
A time series graph with 'Month' on the x-axis and 'Rainfall (mm)' on the y-axis, with points plotted and joined. The trend shows that after an initial rise in March, the average monthly rainfall generally decreases from March to July.
Time series graphs are excellent for visualising trends over time. Always join the points with straight lines.
Common mistakes
- ✗Not including a key for a stem-and-leaf diagram.
- ✗Drawing bars touching in a bar chart (unless it's a histogram, which is for continuous data).
- ✗Failing to label axes or provide a title for the chart.
- ✗Incorrectly calculating angles for pie charts, leading to the sum not being 360°.
- ✗Not ordering the leaves in a stem-and-leaf diagram.
- ✗Using a time series graph for data that does not have a time component.
Exam tips
- ★Always use a ruler and pencil for drawing all charts and diagrams in exams for neatness and accuracy.
- ★Double-check all calculations, especially for pie chart angles, to ensure they sum correctly.
- ★Ensure all labels, titles, and keys are present, clear, and accurate to gain full marks.
- ★When interpreting a chart, refer specifically to the features shown in the diagram (e.g., 'the largest sector in the pie chart shows...', 'the upward trend in the time series graph indicates...').
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