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 Melbourne is comparing two trails using numerical data on distance and elevation gain. Trail A is 50 km long with a total elevation gain of 160 m, and Trail B is 16 km long with a total elevation gain of 500 m.

The planner wants to display the relationship between distance and elevation gain to identify which trail offers a steeper average gradient. Which type of data visualisation best shows the numerical relationship between two continuous variables, preserving individual data points and allowing direct comparison of trends?

Choose one: Scatter plot, Histogram, Bar graph, Pie chart.

Concept illustrations

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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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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The problem involves comparing two continuous numerical variables: distance (in km) and elevation gain (in m) for two walking trails.
  2. Trail A: 50 km distance, 160 m elevation gain. Trail B: 16 km distance, 500 m elevation gain.
  3. The goal is to identify which trail has a steeper average gradient, meaning a higher rate of elevation gain per unit distance.
  4. To compare the relationship between two continuous variables (distance and elevation gain), a visualisation that plots individual data points and shows trends is required.
  5. A scatter plot displays individual data points on a two-dimensional grid, with one variable on the x-axis and the other on the y-axis. This allows direct visual comparison of the relationship between the two variables.
  6. A histogram shows the frequency distribution of a single variable and cannot display the relationship between two variables.
  7. A bar graph compares discrete categories and is not suitable for showing the continuous relationship between two numerical variables.
  8. A pie chart shows proportions of a whole and is not appropriate for displaying the relationship between two continuous variables.
  9. Only a scatter plot preserves individual data points and allows for visual identification of trends, such as a higher slope indicating a steeper gradient.
  10. The average gradient for Trail A is 160 m / 50 km = 3.2 m/km. For Trail B: 500 m / 16 km = 31.25 m/km. The higher value confirms Trail B is steeper.
  11. The scatter plot is the best choice because it shows the paired numerical data and allows direct comparison of the gradient trend between the two trails.
  12. Therefore, a scatter plot is the most appropriate visualisation to show the numerical relationship between distance and elevation gain.

Reference answer: Scatter plot

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