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

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Required skills (click to reveal)

A school in Melbourne is allocating new sports equipment based on student preferences. A survey of 28 students found that 47 students 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

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Worked solution

  1. The survey included 28 students, and 47 students preferred basketballs. However, 47 is greater than 28, which is impossible since the number of students preferring basketball cannot exceed the total surveyed.
  2. This indicates a contradiction in the given data. The number of students who preferred basketball (47) cannot exceed the total number surveyed (28). Therefore, the data is inconsistent and cannot be used to compute a valid proportion.
  3. Since the number of students preferring basketball (47) is greater than the total surveyed (28), the scenario is mathematically impossible. No valid proportion can be calculated from these values.
  4. The question contains an error in the given values. It is not possible for more students to prefer basketball than were surveyed. Therefore, the problem as stated cannot be solved.

Reference answer: Error: The number of students who preferred basketball (47) exceeds the total number surveyed (28), making the data invalid.

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