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

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In a community garden in Melbourne, 42 plots are allocated for vegetable growing and 11 plots are reserved for native pollinator plants. The garden committee wants to display the proportional relationship between these two plot types to inform future planning.

Which type of data visualisation is most appropriate for clearly showing the proportional relationship between two categorical data sets?

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

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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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The data consists of two categorical groups: vegetable plots (42) and native pollinator plots (11). The goal is to show the proportional relationship between these two groups.
  2. Categorical data is best displayed using visualisations that compare parts of a whole or compare group sizes. The two groups are mutually exclusive and represent parts of the total garden.
  3. A pie chart is designed to show proportions of a whole, where each slice represents a category's share of the total. This makes it ideal for comparing parts of a whole.
  4. A bar graph can compare group sizes but does not inherently show proportion as clearly as a pie chart. It is better for comparing absolute values across categories.
  5. A histogram is used for continuous numerical data, not categorical data. It shows frequency distribution of numerical values, so it is not appropriate here.
  6. A stem-and-leaf plot is used to display the distribution of numerical data, particularly for small datasets. It is not suitable for categorical data.
  7. The total number of plots is 42 + 11 = 53. The proportion of vegetable plots is 42/53 ≈ 79.2%, and pollinator plots are 11/53 ≈ 20.8%.
  8. A pie chart visually represents these proportions as angles of slices, making it easy to see that vegetable plots dominate the garden.
  9. The question asks for the most appropriate visualisation to clearly show the proportional relationship between two categorical data sets.
  10. Among the options, only the pie chart is specifically designed to show proportions of a whole for categorical data.
  11. Therefore, the pie chart is the most appropriate choice because it directly represents the proportional relationship between the two categories.
  12. The correct visualisation for showing proportional relationships between two categorical data sets is a pie chart.

Reference answer: Pie chart

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