NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Statistical investigations

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A statistical investigation was conducted in Brisbane to examine the effect of a new study method on test scores. A group of 15 Year 7 students used the method for one week, and their test scores (out of 100) were recorded as: 72, 78, 81, 75, 79, 80, 76, 77, 82, 74, 78, 80, 79, 76, 81.

Calculate the exact interquartile range (IQR) of the test scores. Express your answer as a simplified fraction or integer.

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Worked solution

  1. List the test scores in ascending order: 72, 74, 75, 76, 76, 77, 78, 78, 79, 79, 80, 80, 81, 81, 82.
  2. There are 15 data points, which is an odd number. The median (Q2) is the 8th value in the ordered list.
  3. The 8th value is 78, so Q2 = 78.
  4. To find Q1 (first quartile), consider the lower half of the data, excluding the median. The lower half consists of the first 7 values: 72, 74, 75, 76, 76, 77, 78.
  5. The median of the lower half (Q1) is the 4th value in this subset. The 4th value is 76.
  6. To find Q3 (third quartile), consider the upper half of the data, excluding the median. The upper half consists of the last 7 values: 79, 79, 80, 80, 81, 81, 82.
  7. The median of the upper half (Q3) is the 4th value in this subset. The 4th value is 80.
  8. The interquartile range (IQR) is calculated as IQR = Q3 - Q1.
  9. Substitute the values: IQR = 80 - 76.
  10. Perform the subtraction: 80 - 76 = 4.
  11. The IQR is 4, which is already an integer and does not need to be expressed as a fraction.
  12. The interquartile range of the test scores is exactly 4.

Reference answer: 4

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