To determine which statement about Ella's data must be correct, let's analyze the context of the data collection and the properties of distributions typically found in such scenarios.
1. Ella's data can be described using the mean.
- While it is true that the mean is a useful measure, it provides a central value around which the data points may cluster. However, the mean alone does not capture the shape or spread of the distribution.
2. Ella's data can be described using the maximum value.
- The maximum value only provides information about the highest observation in the dataset. It does not give a complete picture of the overall distribution or provide a summary of the data characteristics.
3. The distribution of Ella's data can be described as having a large spread.
- When asking 100 randomly selected people about the number of school music concerts they attended, we can expect a wide range of responses. Some people may attend many concerts, while others may attend none. This scenario suggests a large spread, where responses vary significantly, indicating high variability in the data.
4. The distribution of Ella's data can be described as having a symmetrical shape.
- While it is possible for data to be symmetrical, it is not a certainty in this case. The distribution can be skewed, especially if, for example, a large number of respondents attended zero concerts.
Given these evaluations, the most correct statement about Ella's data is:
The distribution of Ella's data can be described as having a large spread.
This choice correctly captures the expected variability in the number of school music concerts attended by different individuals, reflecting a broader and more accurate picture of the distribution.
