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

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A school in Sydney orders two types of digital thermometers for Year 9 science experiments. The response times (in seconds) for 12 Type A thermometers are: 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42.

The response times for 12 Type B thermometers are: 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 72. Both data sets are ordered.

For a data set with 12 values, the lower quartile (Q1) is the average of the 3rd and 4th values, and the upper quartile (Q3) is the average of the 9th and 10th values. Calculate the exact interquartile range (IQR) for the Type B response times.

The IQR is the difference between Q3 and Q1.

Concept illustrations

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A five-number summary. Illustrative five-number summary: minimum 1, Q1 4, median 7, Q3 10, maximum 13. IQR = 10 − 4 = 6. Whiskers use the minimum/maximum convention.1471013IQR = Q3 − Q1 = 6
Illustrative five-number summary: minimum 1, Q1 4, median 7, Q3 10, maximum 13. IQR = 10 − 4 = 6. Whiskers use the minimum/maximum convention.
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.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The response times for Type B thermometers are given in ascending order: 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 72.
  2. The data set has 12 values, so the lower quartile (Q1) is the average of the 3rd and 4th values.
  3. The 3rd value is 32 and the 4th value is 33. Q1 = (32 + 33) / 2 = 65 / 2 = 32.5 seconds.
  4. The upper quartile (Q3) is the average of the 9th and 10th values.
  5. The 9th value is 38 and the 10th value is 39. Q3 = (38 + 39) / 2 = 77 / 2 = 38.5 seconds.
  6. The interquartile range (IQR) is calculated as IQR = Q3 - Q1.
  7. Substitute the values: IQR = 38.5 - 32.5 = 6.0 seconds.
  8. The result is exact: 6.0 seconds, which is equivalent to 6 seconds.

Reference answer: 6

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