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

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The weekly water consumption (in kilolitres) for 10 households in Perth and 10 households in Darwin is recorded. The Perth data set is: 12.5, 13.0, 13.5, 14.0, 14.5, 15.0, 15.5, 16.0, 16.5, 17.0.

The Darwin data set is: 11.0, 12.0, 12.5, 13.0, 13.5, 14.0, 14.5, 15.0, 15.5, 18.0. Both data sets are ordered.

Calculate the exact interquartile range (IQR) for the Darwin data set. The IQR is the difference between the upper quartile (Q3) and the lower quartile (Q1).

For a data set with 10 values, Q1 is the 3rd value and Q3 is the 8th value.

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Worked solution

  1. The Darwin data set has 10 values and is already ordered: 11.0, 12.0, 12.5, 13.0, 13.5, 14.0, 14.5, 15.0, 15.5, 18.0.
  2. The lower quartile (Q1) is the 3rd value in a data set of 10 values, as per the given instruction.
  3. The 3rd value in the Darwin data set is 12.5 kilolitres.
  4. The upper quartile (Q3) is the 8th value in a data set of 10 values, as per the given instruction.
  5. The 8th value in the Darwin data set is 15.0 kilolitres.
  6. The interquartile range (IQR) is calculated as Q3 minus Q1.
  7. Substitute the values: IQR = 15.0 - 12.5.
  8. Perform the subtraction: 15.0 - 12.5 = 2.5.
  9. The result is in kilolitres, the unit of water consumption.
  10. The IQR for the Darwin data set is 2.5 kilolitres.
  11. Verify: Q1 = 12.5, Q3 = 15.0, difference = 2.5. Correct.
  12. The interquartile range for the Darwin data set is 2.5 kilolitres.

Reference answer: 2.5

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