Final answer:
The set of scores with the least amount of variability is set (a) 1, 1, 1, 3, as the numbers in this set are very close to each other and vary by only 2 points, indicating very low variability.
Step-by-step explanation:
The student's question revolves around identifying which set of scores contains the least amount of variability. Variability in a data set refers to how spread out the data points are. A set with little variability will have numbers that are close to each other and to the mean of the set.
- (a) 1, 1, 1, 3
- (b) 15, 15, 15, 16
- (c) 5, 11, 32, 21
- (d) 12, 14, 15, 13
When we analyze the sets, set (a) has numbers that are very close, varying only by 2 points. Set (b) has a mean of 15 and numbers differing by at most 1 point. Set (c) has a wide range, with a difference of 27 points between its smallest and largest values. Lastly, set (d) has numbers falling within a 3-point range.
Therefore, the set with the least variability is set (a) since all numbers are either 1 or 3, which is the smallest range of values among all the options provided.