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

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A group of 14 students in Darwin recorded the distance (in metres) they walked during a school fitness challenge. The distances were: 36, 36, 36, 36, 36, 39, 39, 39, 39, 39, 39, 39, 39, 39.

Construct a stem-and-leaf plot using the tens digit as the stem and the units digit as the leaf.

What is the exact value of the mode of the distances walked?

Concept illustrations

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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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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The data consists of 14 distances in metres walked by students in Darwin: 36, 36, 36, 36, 36, 39, 39, 39, 39, 39, 39, 39, 39, 39.
  2. To construct a stem-and-leaf plot, the tens digit is the stem and the units digit is the leaf. For 36, the stem is 3 and the leaf is 6. For 39, the stem is 3 and the leaf is 9.
  3. List all values grouped by stem (tens digit). The only stem is 3, as all values are between 30 and 39.
  4. For stem 3, record the leaves: five 6s (from 36) and nine 9s (from 39).
  5. The stem-and-leaf plot is: 3 | 6 6 6 6 6 9 9 9 9 9 9 9 9 9.
  6. The mode is the value that appears most frequently in a data set.
  7. Count the frequency of each value: 36 appears 5 times, 39 appears 9 times.
  8. Since 39 appears more times than 36, it is the most frequent value.
  9. Therefore, the mode is 39 metres.
  10. Check: 5 occurrences of 36, 9 of 39. 9 > 5, so 39 is the mode.
  11. The mode is exactly 39 metres, as it is the most frequent value.
  12. Final answer: the mode is 39 metres.

Reference answer: 39 m

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