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 compares the average daily walking distance among Year 9 students in Melbourne and Sydney. A random sample of 46 students in Melbourne reported a total walking distance of 1,150 km over one week.

A separate random sample of 38 students in Sydney reported a total of 950 km 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 and answer (click to reveal)

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Worked solution

  1. The total walking distance for Melbourne students is 1,150 km over 7 days, so the total daily walking distance for Melbourne is 1,150 km ÷ 7 days.
  2. Calculate 1,150 ÷ 7: 7 × 164 = 1,148, so 1,150 ÷ 7 = 164 and 2/7 km per day.
  3. The total walking distance for Sydney students is 950 km over 7 days, so the total daily walking distance for Sydney is 950 km ÷ 7 days.
  4. Calculate 950 ÷ 7: 7 × 135 = 945, so 950 ÷ 7 = 135 and 5/7 km per day.
  5. The combined total walking distance for both groups over 7 days is 1,150 km + 950 km = 2,100 km.
  6. The combined number of students is 46 + 38 = 84.
  7. The combined total walking distance over 7 days is 2,100 km, so the combined mean daily walking distance is 2,100 km ÷ 7 days = 300 km per day.
  8. The combined mean daily walking distance for all 84 students is 300 km ÷ 84 students.
  9. Simplify 300 ÷ 84: divide numerator and denominator by 12, giving 25 ÷ 7.
  10. 25 ÷ 7 = 3 and 4/7, so as an improper fraction, it is 25/7.
  11. The fraction 25/7 is already in simplest form because 25 and 7 share no common factors other than 1.
  12. The exact combined mean daily walking distance for the two samples is 25/7 km.

Reference answer: 25/7 km

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