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

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A school in Brisbane is allocating sports equipment based on student preferences. A random sample of 19 students was surveyed, and 88% preferred football over basketball.

What is the exact number of students in the sample who prefer football? Express your answer as a simplified fraction or whole number.

Concept illustrations

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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.
Comparing three category counts. Illustrative category counts: A = 2, B = 4, C = 9. Separate bars compare categories; the vertical scale starts at zero.05102A4B9C5
Illustrative category counts: A = 2, B = 4, C = 9. Separate bars compare categories; the vertical scale starts at zero.

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Worked solution

  1. The survey sampled 19 students, and 88% preferred football. The task is to find the exact number of students who prefer football.
  2. Convert the percentage 88% to a decimal by dividing by 100: 88 ÷ 100 = 0.88.
  3. Multiply the total sample size (19) by the decimal form of the percentage (0.88): 19 × 0.88.
  4. Perform the multiplication: 19 × 0.88 = 16.72.
  5. Since the number of students must be a whole number, and 16.72 is not an integer, check whether 88% of 19 can be expressed as a simplified fraction.
  6. Express 88% as a fraction: 88/100 = 22/25.
  7. Multiply the fraction 22/25 by the sample size 19: (22/25) × 19.
  8. Compute the product: (22 × 19) / 25 = 418 / 25.
  9. Simplify 418 ÷ 25: 25 × 16 = 400, remainder 18, so 418/25 = 16 18/25.
  10. Since 16 18/25 is not a whole number, and the number of students must be an integer, the result 16.72 cannot represent an actual count of students.
  11. Re-evaluate: 88% of 19 must be a whole number because it represents a count of people. Therefore, 88% of 19 must be rounded to the nearest whole number, but the question asks for the 'exact' number.
  12. Since 418/25 = 16.72 is not a whole number, and no integer value of students can yield exactly 88% of 19, the data must be approximate. However, the question states 88% was found in a sample of 19, so the exact number must be the integer closest to 16.72, which is 17. But 17/19 = 0.8947 ≈ 89.5%, not 88%. 16/19 ≈ 84.2%. Therefore, 88% of 19 cannot be an exact integer count. The only way to resolve this is to assume the 88% is rounded, and the exact number must be 17, as it is the closest integer to 16.72.

Reference answer: 17

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