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 Melbourne is comparing the weekly sales (in AUD) of two product categories over 10 weeks. Category A has sales values: 83, 85, 87, 88, 89, 90, 91, 92, 93, 94.

Category B has sales values: 51, 53, 55, 56, 57, 58, 59, 60, 61, 62. 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 analyst has two numerical data sets: Category A (83, 85, 87, 88, 89, 90, 91, 92, 93, 94) and Category B (51, 53, 55, 56, 57, 58, 59, 60, 61, 62). Both are numerical, discrete, and consist of 10 values each.
  2. The goal is to display the shape, centre, and spread of these data sets while preserving individual values. This means the display must show each data point clearly and allow for visual assessment of central tendency and variability.
  3. A histogram groups data into bins and loses individual values. It shows shape and spread but not individual data points. Therefore, it does not preserve individual values.
  4. A bar graph is used for categorical data. These data are numerical and continuous in range, so a bar graph is not appropriate and does not preserve individual values.
  5. A pie chart is used for categorical data showing proportions of a whole. These are numerical sales values, not parts of a whole, so a pie chart is inappropriate.
  6. A stem-and-leaf plot displays each individual value, separates data into stems (tens) and leaves (units), and shows the shape of the distribution. It preserves all original values and allows easy identification of centre (median) and spread (range).
  7. For Category A, the stem is 8 and leaves are 3, 5, 7, 8, 9, 0, 1, 2, 3, 4. For Category B, stem is 5 and leaves are 1, 3, 5, 6, 7, 8, 9, 0, 1, 2. Each value is visible.
  8. The stem-and-leaf plot allows direct comparison of shape (both are roughly symmetric), centre (median of A is 89.5, B is 57.5), and spread (range of A is 11, B is 11).
  9. The stem-and-leaf plot is the only option that preserves individual values while clearly showing shape, centre, and spread.
  10. Therefore, the stem-and-leaf plot is the most appropriate display for this context.
  11. The final answer is 'Stem-and-leaf plot' because it best meets the criteria of showing shape, centre, spread, and preserving individual values.
  12. All other options fail to preserve individual values or are inappropriate for numerical data. The stem-and-leaf plot is the only valid choice.

Reference answer: Stem-and-leaf plot

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