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

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Required skills (click to reveal)

In a community garden in Melbourne, a statistical investigation was conducted to compare the weekly yield (in kilograms) of two types of tomato plants over 8 weeks. Type A plants yielded 44 kg, 46 kg, 48 kg, 44 kg, 45 kg, 47 kg, 44 kg, and 46 kg.

Type B plants yielded 42 kg, 44 kg, 43 kg, 45 kg, 44 kg, 46 kg, 44 kg, and 43 kg. Calculate the exact mean yield for Type B tomato plants.

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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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. List the weekly yields for Type B tomato plants: 42 kg, 44 kg, 43 kg, 45 kg, 44 kg, 46 kg, 44 kg, 43 kg.
  2. Sum all the yields: 42 + 44 + 43 + 45 + 44 + 46 + 44 + 43.
  3. Perform the addition step by step: 42 + 44 = 86; 86 + 43 = 129; 129 + 45 = 174; 174 + 44 = 218; 218 + 46 = 264; 264 + 44 = 308; 308 + 43 = 351.
  4. The total yield over 8 weeks is 351 kg.
  5. Divide the total yield by the number of weeks to find the mean: 351 ÷ 8.
  6. Express the division as a fraction: 351/8.
  7. Check if the fraction can be simplified. The greatest common divisor of 351 and 8 is 1, so 351/8 is already in simplest form.
  8. The mean yield is 351/8 kg.
  9. Verify the sum: 42 + 44 = 86, 86 + 43 = 129, 129 + 45 = 174, 174 + 44 = 218, 218 + 46 = 264, 264 + 44 = 308, 308 + 43 = 351. Correct.
  10. Verify division: 8 × 43 = 344, 351 − 344 = 7, so 351/8 = 43 and 7/8. This confirms 351/8 is correct.
  11. The exact mean yield for Type B tomato plants is 351/8 kg.
  12. Final answer: 351/8 kg.

Reference answer: 351/8 kg

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