To determine how to measure the center of the data for both Rome and New York correctly, let's analyze the given statistical measures, focusing especially on the median, mean, and IQR (Interquartile Range). These measures will help us decide which central tendency measure best represents each dataset.
### Rome Data Analysis:
- Maximum: 16
- Minimum: 0
- Q1 (First Quartile): 3
- Q3 (Third Quartile): 13
- IQR (Interquartile Range): 10
- Median: 8.5
- Mean: 8
- Mode (Most Frequent Value): 5.4
### New York Data Analysis:
- Maximum: 20
- Minimum: 1
- Q1 (First Quartile): 4.5
- Q3 (Third Quartile): 6
- IQR (Interquartile Range): 1.5
- Median: 5.5
- Mean: 7.25
- Mode (Most Frequent Value): 5.4
### Determining the Best Measure of Center:
1. Rome Data:
- Mean: 8
- Median: 8.5
- IQR: 10 (significant spread)
The high IQR of 10 suggests that there is a wide range of values around the median in the Rome data, indicating possible skewness or outliers. In such cases, the median generally provides a better measure of central tendency as it is less affected by extreme values.
2. New York Data:
- Mean: 7.25
- Median: 5.5
- IQR: 1.5 (small spread)
The lower IQR of 1.5 indicates that the data around the median is more tightly clustered and suggests fewer outliers or less skewness by comparison. However, in this case, the median can still be more robust as it isn’t influenced as much by outliers compared to the mean, although the difference between the mean and median is smaller.
Given these analyses:
- For Rome, due to the high IQR and potential influence of outliers, the median is a more descriptive measure of the center.
- For New York, despite the smaller IQR suggesting less presence of outliers, the median remains a resistant measure unaffected by extreme values.
### Conclusion:
Both centers are best described with the median, as the median provides a robust measure of central tendency that is less influenced by potential outliers for both datasets.
Thus, the correct choice is:
Both centers are best described with the median.
