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

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A statistical investigation is conducted to compare the average walking distance per day among Year 9 students in Melbourne and Sydney. A random sample of 37 students in Melbourne reported a total walking distance of 1,147 kilometres over one week, and a random sample of 58 students in Sydney reported a total of 1,856 kilometres over the same period.

What is the exact combined mean daily walking distance (in km) for the two samples? Express your answer as a simplified fraction.

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 total walking distance for Melbourne students over one week is 1,147 km, and there are 37 students in the sample.
  2. The total walking distance for Sydney students over one week is 1,856 km, and there are 58 students in the sample.
  3. To find the combined mean daily walking distance, first calculate the total walking distance across both cities: 1,147 km + 1,856 km = 3,003 km.
  4. Next, calculate the total number of students: 37 + 58 = 95 students.
  5. The total walking distance was recorded over 7 days, so to find the total daily walking distance across both samples, divide the weekly total by 7: 3,003 km ÷ 7 = 429 km per day.
  6. Now, compute the mean daily walking distance for the combined sample: divide the total daily walking distance by the total number of students: 429 km ÷ 95.
  7. Perform the division: 429 ÷ 95. First, express as a fraction: 429/95.
  8. Simplify the fraction 429/95. Check for common factors. The prime factorisation of 429 is 3 × 11 × 13. The prime factorisation of 95 is 5 × 19. No common factors exist, so the fraction is already in simplest form.
  9. The combined mean daily walking distance is 429/95 km.
  10. Verify the calculation: 95 × 4 = 380, 429 − 380 = 49. So 429/95 = 4 and 49/95. This confirms the fraction is correct.
  11. The exact combined mean daily walking distance for the two samples is 429/95 km.
  12. The result is a simplified fraction and matches the required format.

Reference answer: 429/95 km

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