Final answer:
Adding 3 to each score in a set does not change the range, as both the lowest and highest values are increased by the same amount. Halving each score decreases the range by a factor of two. The correct answer, with an amendment, is option c) i) Has no effect, ii) Decreases.
Step-by-step explanation:
The student has asked about the effect on the range of a set of data when certain operations are performed on each score in the set. The range is the difference between the highest and lowest values in a set of numbers.
Adding the same number (in this case, 3) to each score in the data set will not affect the range because both the smallest and largest numbers will be increased by the same amount, thus maintaining the same difference between them. Therefore, the range will remain unchanged.
On the other hand, halving each score in the data set will decrease the range because it scales down the difference between the highest and lowest values by a factor of two.
So, if we translate this to the possible effects mentioned in the original question:
- Adding 3 to each score will have no effect on the range.
- Halving each score will decrease the range.
Therefore, the correct answer to the student's question is that option c) i) Increases, ii) Decreases is the one that correctly identifies the effect on the range, except that option i) should state that the range remains unchanged, rather than increases.