GRE General TestQuantitative ReasoningHard
A data analyst is examining a set of scores: 10, 15, 20, 25, 30. If each score in the set is multiplied by 2 and then 5 is added to each new score, what is the new mean of the modified set?
- A45
- B40
- C55
- D50
Show answer & explanationAnswer & explanation
Correct answer: A. 45
When a data set is transformed by multiplying each value by 'a' and adding 'b', the new mean will be 'a' times the original mean plus 'b'.
Why the other options are wrong
- B. This is the original mean multiplied by 2, without adding 5.
- C. This is likely a calculation error or misunderstanding of the transformation.
- D. This is the original mean multiplied by 2 and then 10 is added, or an error in calculation.
Effect of Transformations on Mean
If each value in a data set is transformed by multiplying by a constant 'a' and then adding a constant 'b', the new mean is found by applying the same transformation to the original mean.
- New Mean = a * (Original Mean) + b.
- This property applies to transformations of the form y = ax + b.
- It simplifies calculating the mean of transformed data without re-calculating all values.
Memory trick: Mean's Magic Rule: Whatever you do to each number, do to the mean!