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 group of 17 students in Adelaide recorded the time (in seconds) it took them to complete a 400-metre sprint. The recorded times are: 52.3, 53.1, 53.4, 53.6, 53.8, 54.0, 54.2, 54.5, 54.7, 54.9, 55.1, 55.3, 55.6, 55.8, 56.0, 56.4, 57.2.

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 time?

Express your answer as a simplified fraction.

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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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The data set contains 17 times in seconds, recorded for a 400-metre sprint in Adelaide. The times are: 52.3, 53.1, 53.4, 53.6, 53.8, 54.0, 54.2, 54.5, 54.7, 54.9, 55.1, 55.3, 55.6, 55.8, 56.0, 56.4, 57.2.
  2. To construct a stem-and-leaf plot, the stem is the whole number part (tens and units), and the leaf is the decimal part (tenths). For example, 52.3 has stem 52 and leaf 3.
  3. List all stems from 52 to 57, as these are the whole number parts of the times. For each time, write the decimal part as the leaf next to its stem.
  4. Stem 52: leaf 3 → 52.3
  5. Stem 53: leaves 1, 4, 6, 8 → 53.1, 53.4, 53.6, 53.8
  6. Stem 54: leaves 0, 2, 5, 7, 9 → 54.0, 54.2, 54.5, 54.7, 54.9
  7. Stem 55: leaves 1, 3, 6, 8 → 55.1, 55.3, 55.6, 55.8
  8. Stem 56: leaves 0, 4 → 56.0, 56.4
  9. Stem 57: leaf 2 → 57.2
  10. The data is already in ascending order. The median is the 9th value in a list of 17 values (since (17+1)/2 = 9).
  11. Count to the 9th value: 1st: 52.3, 2nd: 53.1, 3rd: 53.4, 4th: 53.6, 5th: 53.8, 6th: 54.0, 7th: 54.2, 8th: 54.5, 9th: 54.7.
  12. The median time is 54.7 seconds. As a simplified fraction, 54.7 = 547/10. This fraction is already in simplest form because 547 and 10 share no common factors other than 1.

Reference answer: 547/10

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