NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Sampling methods and bias

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A school in Melbourne is planning to order new sports equipment based on student preferences. A survey of 52 students found that 49 preferred basketballs over footballs.

What is the exact proportion of surveyed students who preferred basketballs? Express your answer as a simplified fraction.

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A sample is part of a population. The large outline represents a population of 24 members. Six filled members illustrate a sample. This picture does not establish that a selection process was random.6 selected from 24
The large outline represents a population of 24 members. Six filled members illustrate a sample. This picture does not establish that a selection process was random.
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 survey included 52 students, and 49 of them preferred basketballs.
  2. The proportion of students who preferred basketballs is calculated as the number who preferred basketballs divided by the total number surveyed.
  3. Substitute the values: proportion = 49 / 52.
  4. Simplify the fraction 49/52 by finding the greatest common divisor (GCD) of 49 and 52.
  5. Factor 49: 49 = 7 × 7. Factor 52: 52 = 2 × 2 × 13. There are no common prime factors between 49 and 52.
  6. Since the GCD is 1, the fraction 49/52 is already in its simplest form.
  7. The exact proportion is therefore 49/52.
  8. Verify by checking that 49 and 52 share no common factors other than 1.
  9. 49 is 7², and 52 is 2² × 13. No common prime factors exist.
  10. The fraction 49/52 cannot be simplified further.
  11. The exact proportion of surveyed students who preferred basketballs is 49/52.
  12. This matches the requirement to express the answer as a simplified fraction.

Reference answer: 49/52

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