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

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A statistical investigation is conducted in Adelaide to estimate the average number of minutes per day that residents spend using public transport. A random sample of 18 households is selected, and the total time spent on public transport by all households in the sample over one day is recorded as 1620 minutes.

What is the exact mean number of minutes per household in the sample?

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Explanation

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Worked solution

  1. The total time spent on public transport by all 18 households in the sample is 1620 minutes.
  2. To find the mean number of minutes per household, divide the total time by the number of households.
  3. The formula for the mean is: mean = total sum / number of items.
  4. Substitute the given values: mean = 1620 minutes / 18 households.
  5. Perform the division: 1620 ÷ 18.
  6. Simplify the fraction: 1620 / 18.
  7. Divide both numerator and denominator by 6: 1620 ÷ 6 = 270, 18 ÷ 6 = 3.
  8. Now compute 270 / 3 = 90.
  9. The result is 90 minutes per household.
  10. Check: 18 households × 90 minutes = 1620 minutes, which matches the total.
  11. The mean number of minutes per household in the sample is exactly 90 minutes.
  12. The calculation is exact and no rounding is needed.

Reference answer: 90 minutes

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