NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Boxplots and distribution comparisons

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A craft designer in Brisbane creates two series of handmade ceramic tiles, each containing 25 tiles. The thickness of each tile (in millimetres) is measured and summarised using boxplots.

For Series A, the five-number summary is: minimum = 33.0, Q1 = 36.0, median = 38.5, Q3 = 42.0, maximum = 47.5. For Series B, the five-number summary is: minimum = 33.0, Q1 = 37.5, median = 40.0, Q3 = 45.0, maximum = 52.5.

Both data sets are continuous numerical variables. Using the five-number summaries, calculate the exact interquartile range (IQR) for Series B.

Provide the answer as a single exact number.

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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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The interquartile range (IQR) is defined as the difference between the upper quartile (Q3) and the lower quartile (Q1) of a data set.
  2. For Series B, the five-number summary provides Q1 = 37.5 mm and Q3 = 45.0 mm.
  3. The formula for IQR is IQR = Q3 - Q1.
  4. Substitute the values: IQR = 45.0 - 37.5.
  5. Perform the subtraction: 45.0 - 37.5 = 7.5.
  6. The result is 7.5 mm, which is the exact interquartile range for Series B.
  7. The IQR is a measure of spread and is expressed in the same units as the data, which is millimetres.
  8. No further calculations or conversions are needed as the values are already in decimal form and the subtraction is exact.
  9. The result 7.5 is a terminating decimal and represents the exact IQR.
  10. The answer is confirmed as 7.5 mm, which matches the requirement for an exact number.
  11. The interquartile range for Series B is 7.5 mm.
  12. The final answer is 7.5 mm, which is a single exact number as required.

Reference answer: 7.5

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