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 10 girls and 10 boys in a Year 9 class are recorded. The girls' heights are: 158, 160, 162, 162, 163, 164, 165, 166, 167, 170.

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

Calculate the exact median height for the boys' data set.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The boys' heights are given as: 160, 162, 163, 164, 165, 166, 167, 168, 170, 172. This is a list of 10 values, which is even.
  2. To find the median of an even-numbered data set, we take the average of the 5th and 6th values when the data is ordered from smallest to largest.
  3. The data is already in ascending order: 160, 162, 163, 164, 165, 166, 167, 168, 170, 172.
  4. The 5th value is 165 cm.
  5. The 6th value is 166 cm.
  6. To find the median, calculate the average of 165 and 166: (165 + 166) / 2.
  7. Add the two values: 165 + 166 = 331.
  8. Divide the sum by 2: 331 / 2 = 165.5.
  9. The result is 165.5 cm, which is the median height for the boys.
  10. Check: the 5th and 6th values are correctly identified, and the average is computed exactly.
  11. The median height for the boys is 165.5 cm.
  12. Final answer confirmed: 165.5 cm.

Reference answer: 165.5 cm

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