To determine the best measure of the center for the data provided about the number of times families eat at restaurants during a week, we need to compare the mean and median for each city to see how they describe the central tendency of the data.
### Analysis for Rome:
- Mean: 6.4
- Median: 6.5
In Rome, the mean and median are fairly close to each other (6.4 and 6.5, respectively). When the mean and median are close in value, it typically indicates that the data does not have significant skewness or outliers. This closeness suggests that either measure could be appropriate, but using the mean can often be more informative as it takes into account every data point, providing a more complete measure of central tendency. Thus, the mean is a suitable measure for describing the center of the data for Rome.
### Analysis for New York:
- Mean: 6.1
- Median: 5.5
In New York, there is a noticeable difference between the mean (6.1) and the median (5.5). This gap suggests that the data may be skewed or contain outliers. The mean is more susceptible to the effects of skewness and outliers, which can distort the central tendency it represents. The median, however, is a measure that is less affected by such factors and provides a better representation of the center in such situations.
### Conclusion:
Given the comparison, we can conclude the following:
- For Rome, the mean is the best measure of the center since the mean and median are very close to each other.
- For New York, the median is the best measure of the center since there is a significant difference between the mean and the median, indicating potential skewness or outliers.
Therefore, the best description for measuring the center of these data is:
"The Rome data center is best described by the mean. The New York data center is best described by the median."
