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

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A school in Perth is ordering art supplies for a year-long project. The order includes 29 boxes of acrylic paints and 49 boxes of canvas sheets.

The school wants to display the proportional relationship between these two items to justify the budget allocation. Which type of display 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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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The school is comparing two categorical data sets: 29 boxes of acrylic paints and 49 boxes of canvas sheets. These are discrete counts of different types of art supplies.
  2. The goal is to display the proportional relationship between these two items to justify budget allocation, meaning the relative sizes of the two categories must be clearly visible.
  3. A pie chart shows parts of a whole as sectors of a circle, making it ideal for displaying proportions of categorical data where the sum of parts equals 100%.
  4. A bar graph can compare quantities across categories, but it does not inherently show proportion as clearly as a pie chart when the focus is on relative size within a whole.
  5. A histogram is used for continuous numerical data grouped into intervals, not for categorical data like types of art supplies.
  6. A stem-and-leaf plot is used to display the distribution of numerical data, particularly for small data sets, and is not suitable for categorical comparisons.
  7. Since the data are categorical and the purpose is to show proportion (i.e., how much of the total budget is allocated to each item), a pie chart is the most appropriate choice.
  8. The total number of boxes is 29 + 49 = 78. The proportion of acrylic paints is 29/78 ≈ 37.2%, and canvas sheets is 49/78 ≈ 62.8%.
  9. A pie chart visually represents these proportions as sector angles, making it easy to see that canvas sheets make up a larger share of the order.
  10. The pie chart clearly shows the proportional relationship between the two items, which supports the budget justification by illustrating relative importance.
  11. Therefore, the most appropriate display for showing the proportional relationship between two categorical data sets is a pie chart.
  12. The final answer is pie chart, as it best represents the proportion of one category relative to the whole.

Reference answer: Pie chart

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