NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
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Population investigations

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A school in Brisbane is conducting a statistical investigation to estimate the average number of notebooks used per student per semester. A random sample of 41 students is selected, and the total number of notebooks used by the sample over one semester is 70.

What is the exact mean number of notebooks used per student in the sample?

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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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The total number of notebooks used by the sample of 41 students is given as 70.
  2. To find the mean number of notebooks per student, divide the total number of notebooks by the number of students in the sample.
  3. The formula for the mean is: mean = total sum / number of items.
  4. Substitute the given values: mean = 70 / 41.
  5. Perform the division: 70 ÷ 41.
  6. 70 divided by 41 equals approximately 1.7073170731707317.
  7. Since the question asks for the exact mean, express the result as a fraction.
  8. 70 and 41 have no common factors other than 1, so the fraction 70/41 is already in simplest form.
  9. The exact mean number of notebooks used per student is 70/41.
  10. Verify by multiplying the mean by the number of students: (70/41) × 41 = 70, which matches the total.
  11. The calculation confirms that the mean is exactly 70/41 notebooks per student.
  12. The exact mean number of notebooks used per student in the sample is 70/41.

Reference answer: 70/41

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