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 data analyst in Brisbane is comparing the weekly rainfall (in mm) for two regions over 10 weeks. Region A has rainfall values: 22, 24, 26, 28, 30, 32, 34, 36, 38, 40.

Region B has rainfall values: 86, 88, 90, 92, 94, 96, 98, 100, 102, 104. Which type of display best shows the shape, centre, and spread of these numerical data sets while preserving individual values?

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

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 data consists of numerical rainfall values (in mm) for 10 weeks in two regions, A and B. The values are discrete and ordered, and the goal is to display the shape, centre, and spread of each data set while preserving individual values.
  2. Region A: 22, 24, 26, 28, 30, 32, 34, 36, 38, 40. These are evenly spaced, increasing by 2 mm each week. Region B: 86, 88, 90, 92, 94, 96, 98, 100, 102, 104. Also evenly spaced, increasing by 2 mm each week.
  3. The data is numerical and continuous in nature (rainfall in mm), and both sets contain individual values that should be visible in the display.
  4. A histogram groups data into intervals and loses individual values. It shows shape and spread but not individual data points.
  5. A bar graph is used for categorical data. Rainfall is numerical, not categorical, so a bar graph is not appropriate.
  6. A pie chart is used to show proportions of a whole, typically for categorical data. It is not suitable for numerical data like rainfall over time.
  7. A stem-and-leaf plot displays individual values, shows the shape of the distribution, and allows easy identification of centre (median) and spread (range). It is ideal for small numerical data sets.
  8. For Region A, the stem would be 2, 3, and 4 (tens digit), and leaves would be the units (2, 4, 6, etc.). This preserves all 10 values exactly.
  9. For Region B, stems 8, 9, and 10 (tens and hundreds) would be used. The leaves would again preserve all 10 values.
  10. The stem-and-leaf plot allows direct comparison of shape (both are uniform, symmetric), centre (median of A is 29, B is 93), and spread (range of A is 18 mm, B is 18 mm).
  11. All other options either group values (histogram), represent categories (bar graph, pie chart), or fail to preserve individual data points.
  12. Therefore, the stem-and-leaf plot is the best choice because it shows shape, centre, spread, and preserves individual values for numerical data.

Reference answer: Stem-and-leaf plot

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