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 set?
- A45
- B55
- C50
- D40
Show answer & explanationAnswer & explanation
Correct answer: B. 55
Original mean = (10+15+20+25+30)/5 = 100/5 = 20. When each score is multiplied by 2, the mean is also multiplied by 2: 20 * 2 = 40. When 5 is added to each new score, the mean also increases by 5: 40 + 5 = 45.
Why the other options are wrong
- A. This is the correct new mean after applying both transformations.
- C. This is incorrect; it might result from adding 5 to the original mean then multiplying by 2, or other miscalculations.
- D. This is the mean after only multiplying by 2, without adding 5.
Effect of Transformations on Mean
If each data point in a set is transformed by multiplying by a constant 'a' and then adding a constant 'b' (x' = ax + b), the new mean (μ') will be transformed similarly: μ' = aμ + b.
- Adding/subtracting a constant to each data point changes the mean by that constant.
- Multiplying/dividing each data point by a constant changes the mean by that constant.
- These transformations apply directly to the mean.
Memory trick: Mean follows the same operations as the data.