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 Darwin is allocating new sports equipment based on student preferences. The school has 1200 students and uses a stratified sampling method to survey 37 students from Year 9 and 76 students from Year 10.

The survey found that 37 students in Year 9 and 76 students in Year 10 preferred basketballs. 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 total number of students surveyed is the sum of Year 9 and Year 10 students surveyed: 37 (Year 9) + 76 (Year 10) = 113 students.
  2. The total number of students who preferred basketball is the sum of those from both years: 37 (Year 9) + 76 (Year 10) = 113 students.
  3. The proportion of surveyed students who preferred basketball is calculated as: (number who preferred basketball) / (total surveyed) = 113 / 113.
  4. Simplify the fraction 113/113 by dividing both numerator and denominator by their greatest common divisor, which is 113.
  5. 113 ÷ 113 = 1, and 113 ÷ 113 = 1, so the simplified fraction is 1/1.
  6. The proportion of surveyed students who preferred basketball is therefore 1/1.

Reference answer: 1/1

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