NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Evaluating statistical claims

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Required skills (click to reveal)

A statistical report in Brisbane claims that 39% of residents in a local suburb have been diagnosed with a chronic health condition. The report is based on a survey of 770 randomly selected individuals from the suburb.

What is the exact number of individuals in the sample who were diagnosed with a chronic health condition? Express your answer as an exact integer.

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 report states that 39% of 770 surveyed individuals have a chronic health condition. The percentage must be converted to a decimal for calculation.
  2. Convert 39% to a decimal by dividing by 100: 39 / 100 = 0.39.
  3. Multiply the decimal form of the percentage by the total sample size: 0.39 × 770.
  4. Perform the multiplication: 0.39 × 770 = (39/100) × 770.
  5. Simplify the fraction: (39 × 770) / 100.
  6. Calculate 39 × 770: 39 × 700 = 27,300; 39 × 70 = 2,730; total = 27,300 + 2,730 = 30,030.
  7. Divide 30,030 by 100: 30,030 / 100 = 300.3.
  8. Since the number of individuals must be an integer, and 300.3 is not a whole number, the result must be rounded to the nearest whole number.
  9. Round 300.3 to the nearest integer: 300.3 is closer to 300 than to 301, so the result is 300.
  10. Verify the calculation: 39% of 770 = (39/100) × 770 = 30,030 / 100 = 300.3. Since individuals cannot be fractional, and the original data is from a survey, the exact count must be an integer.
  11. The result 300.3 indicates that the original percentage was likely rounded. The closest integer to 300.3 is 300, so 300 individuals were diagnosed.
  12. Therefore, the exact number of individuals in the sample diagnosed with a chronic health condition is 300.

Reference answer: 300

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