To analyze the data distribution of the ages in the given list (6, 7, 7, 8, 9, 10, 42, 43, 45, 64, 65), let's evaluate the given statements:
A. The data has more than one gap.
- This statement is true because there is a significant gap between the ages of 10 and 42. Additionally, there is another gap between 10 and 64. Therefore, this statement accurately describes the data.
B. The data is spread out.
- This statement is also true. The ages range from 6 to 65, showing a wide variety of ages represented in the family. This indicates that the data is indeed spread out over a large range.
C. The data is symmetric.
- This statement is false. The ages are not symmetrically distributed because the majority of the younger ages (6-10) are clustered to the left, while older ages (42-65) create a gap before the higher values. This results in an asymmetrical distribution.
D. The distribution forms three clusters.
- This statement is somewhat subjective but can be interpreted as false. While there are groupings (younger ages, middle age, and older ages), they do not clearly form distinct clusters in a way that strictly classifies them into three separate groups based on the distribution.
Based on this analysis, the three statements that best describe the data distribution are:
- A. The data has more than one gap.
- B. The data is spread out.
- (The third statement could be open to interpretation, but the most accurate conclusion about clusters is actually weak. Therefore, the best selections remain A and B while C is false, and D is also not a strong description.)
Given the confusion with clustering, A, and B are the best clear statements.
So, to summarize, A and B are the strongest descriptors of the data distribution.