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Question 19

Five numbers have a mean of 8. A sixth number is added and the mean of all six numbers becomes 7. Which statements about this change are true? Select all that apply.

  1. The sixth number is 1, because the mean fell by 1.
  2. The first five numbers total 40.Correct answer
  3. The sixth number must be negative, because the mean went down.
  4. All six numbers together total 42.Correct answer
  5. The sixth number is 2.Correct answer

Explanation

Five numbers averaging 8 total 40, and six numbers averaging 7 total 42, so the number that was added is 42 - 40 = 2. A mean falling by 1 does not make the added number 1, because the new value has to cover a shortfall of 1 spread across all six numbers, which is why comparing the two totals is the reliable route.

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Question 19: Five numbers have a mean of 8. A sixth number is added and… · Statistics and Probability · Questena