NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Comparing data distributions

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The heights (in cm) of 12 girls and 12 boys in a Year 9 class are recorded. The girls' heights are: 158, 160, 162, 162, 163, 164, 165, 165, 166, 167, 168, 170.

The boys' heights are: 160, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 174.

Calculate the exact median height difference between the boys and the girls.

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Worked solution

  1. The heights of 12 girls and 12 boys are given. The median is the middle value of an ordered data set. For an even number of observations, the median is the average of the 6th and 7th values.
  2. List the girls' heights in ascending order: 158, 160, 162, 162, 163, 164, 165, 165, 166, 167, 168, 170.
  3. The 6th value is 164 cm, and the 7th value is 165 cm. The median height for girls is (164 + 165) / 2.
  4. Calculate the girls' median: (164 + 165) / 2 = 329 / 2 = 164.5 cm.
  5. List the boys' heights in ascending order: 160, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 174.
  6. The 6th value is 166 cm, and the 7th value is 167 cm. The median height for boys is (166 + 167) / 2.
  7. Calculate the boys' median: (166 + 167) / 2 = 333 / 2 = 166.5 cm.
  8. Find the difference between the boys' median and the girls' median: 166.5 - 164.5.
  9. Calculate the difference: 166.5 - 164.5 = 2.0 cm.
  10. The median height difference is 2.0 cm, with boys taller than girls.
  11. Verify the median positions: for 12 values, the 6th and 7th are correct. All values are correctly ordered and averaged.
  12. The exact median height difference is 2.0 cm, as both medians were calculated exactly from the data.

Reference answer: 2.0 cm

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