Problem-Solving and Data AnalysisVery hardEffect of raising only the low scores on a mean
Problem-Solving and Data Analysis practice question
A class's test scores have a mean of 70, and at least one score is below 70. The teacher adds 10 points to every score that is below 70 and leaves the other scores unchanged. Which of the following must be true of the new mean?
- A. It is greater than 70.Correct
- B. It is exactly 80.
- C. It is less than 70.
- D. It is exactly 70.
Answer: A. It is greater than 70.
Some scores rise and none fall, so the total, and therefore the mean, rises.
Why the other answers are wrong
- B. It is exactly 80.
- Only some scores rise, so the mean rises by less than 10.
- C. It is less than 70.
- No score decreases.
- D. It is exactly 70.
- At least one score rises, so the mean cannot stay the same.
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