NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Choosing data visualisations

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Required skills (click to reveal)

A walking route planner in Sydney compares two trails: Trail A has a total distance of 69 km with 73 distinct elevation changes recorded, while Trail B has 73 km and 69 elevation changes. The planner wants to display the relationship between trail length and number of elevation changes to identify patterns.

Which data visualisation best shows the numerical relationship between two continuous variables, preserving individual data points and allowing comparison of trends?

Choose one: Scatter plot, Histogram, Pie chart, Stem-and-leaf plot.

Concept illustrations

These are separate worked examples of related concepts, not a diagram of this question. Their values and dimensions do not describe your question.

Comparing three category counts. Illustrative category counts: A = 2, B = 4, C = 9. Separate bars compare categories; the vertical scale starts at zero.05102A4B9C5
Illustrative category counts: A = 2, B = 4, C = 9. Separate bars compare categories; the vertical scale starts at zero.
Median, mode and range in sorted data. The ordered values are 2,3,3,8,9. The middle value is 3, the most frequent value is 3, and the range is 9 − 2 = 7. The row uses equal spacing, not a number-line scale.23389↑ medianmode 3 range 7
The ordered values are 2,3,3,8,9. The middle value is 3, the most frequent value is 3, and the range is 9 − 2 = 7. The row uses equal spacing, not a number-line scale.

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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The scenario involves two continuous numerical variables: trail length (in km) and number of elevation changes. Trail A has 69 km and 73 elevation changes; Trail B has 73 km and 69 elevation changes.
  2. The goal is to display the relationship between two continuous variables, preserve individual data points, and allow comparison of trends.
  3. A scatter plot is used to display the relationship between two continuous variables, with each point representing a pair of values (e.g., length and elevation changes).
  4. A histogram is used to show the frequency distribution of a single numerical variable, not the relationship between two variables.
  5. A pie chart is used to show proportions of a categorical variable, not the relationship between two continuous variables.
  6. A stem-and-leaf plot is used to display the distribution of a single numerical variable, not the relationship between two variables.
  7. Only a scatter plot allows the visualisation of the numerical relationship between two continuous variables, with each data point clearly represented.
  8. The scatter plot enables identification of trends, such as whether longer trails have more elevation changes, and allows comparison of individual data points.
  9. The data points (69, 73) and (73, 69) can be plotted on a scatter plot to visually assess any correlation or pattern.
  10. The scatter plot is the only option that meets all criteria: two continuous variables, preservation of individual data points, and ability to interpret trends.
  11. Therefore, the scatter plot is the most appropriate visualisation for this context.
  12. The correct choice is scatter plot, as it best shows the numerical relationship between two continuous variables while preserving individual data points and enabling trend comparison.

Reference answer: Scatter plot

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