Final answer:
The correct pair of sets where the means are the same and Set A has a smaller standard deviation compared to Set B is option c: Set A = {0, 2, 4, 6, 8}, Set B = {1, 3, 5, 7, 9}. Both have a mean of 4 but Set A, being less spread out around the mean, has a smaller standard deviation.
Step-by-step explanation:
The student has asked to create two sets (Set A and Set B) where the means are the same, but the standard deviation of Set A is smaller than the standard deviation of Set B. Let’s analyze each pair of sets:
- Set A = {2, 4, 6, 8, 10}, Set B = {1, 3, 5, 7, 9}: Both sets have the same mean of 6. However, Set B is more spread out, with each number being one less than the corresponding number in Set A. This would typically result in a larger standard deviation for Set B compared to Set A. However, since the amounts deviate symmetrically and the mean is centrally located, their standard deviations are actually the same.
- Set A = {1, 2, 3, 4, 5}, Set B = {2, 4, 6, 8, 10}: Set A has a mean of 3 while Set B has a mean of 6, so they don’t meet the criteria since the means are not the same.
- Set A = {0, 2, 4, 6, 8}, Set B = {1, 3, 5, 7, 9}: Both sets have a mean of 4. Set A shows less variability around the mean, hence a smaller standard deviation. Set B, on the other hand, is evenly spread out around the mean, leading to a larger standard deviation.
- Set A = {1, 3, 5, 7, 9}, Set B = {2, 4, 6, 8, 10}: Both sets have the same mean of 5, and like the first pair, while Set B has numbers one greater than Set A, their deviations from the mean are symmetric, hence their standard deviations also match.
Only sets under option c meet the criteria where Set A and Set B have the same mean, but Set A has a smaller standard deviation than Set B.