NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Data displays and distributions

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Required skills (click to reveal)

A craft group in Perth made 14 identical wooden coasters. The thickness of each coaster, measured in millimetres, was recorded as: 5.9, 6.2, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.3, 7.5, 7.8.

Construct a stem-and-leaf plot using the whole number part as the stem and the decimal part as the leaf. What is the exact value of the median thickness of the coasters?

Express your answer as a simplified fraction.

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.

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.
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.

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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The thickness values are given in millimetres: 5.9, 6.2, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.3, 7.5, 7.8. There are 14 data points, which is even.
  2. To construct a stem-and-leaf plot, the stem is the whole number part (in mm), and the leaf is the decimal part (in tenths of mm). For example, 5.9 has stem 5 and leaf 9.
  3. List all values by stem: stem 5: 9; stem 6: 2, 4, 5, 6, 7, 8, 9; stem 7: 0, 1, 2, 3, 5, 8.
  4. The stem-and-leaf plot is now complete: 5 | 9; 6 | 2 4 5 6 7 8 9; 7 | 0 1 2 3 5 8.
  5. To find the median, since there are 14 values (even), the median is the average of the 7th and 8th values when ordered.
  6. List the values in order: 5.9, 6.2, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.3, 7.5, 7.8.
  7. The 7th value is 6.8 mm, and the 8th value is 6.9 mm.
  8. Calculate the average: (6.8 + 6.9) / 2 = 13.7 / 2 = 6.85 mm.
  9. Convert 6.85 mm to a simplified fraction: 6.85 = 685/100 = 137/20 mm.
  10. Check that 137 and 20 have no common factors: 137 is prime, 20 = 2^2 * 5, so 137/20 is simplified.
  11. The median thickness is exactly 137/20 mm.
  12. Verify by confirming the 7th and 8th values in the ordered list are 6.8 and 6.9, and their average is 6.85, which equals 137/20.

Reference answer: 137/20 mm

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