Question

The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy or New York, New York:

High   Low   Q1     Q3    IQR   Median    Mean        σ
Rome 18         1        3       7       4         6.5       6.4           4.3
NY      14        1       4.5    8.5      4        5.5        6.1            3.2

Which of the choices below best describes how to measure the center of this data?

- Both centers are best described with the mean.

-Both centers are best described with the median.

- The Rome data center is best described by the mean. The New York data center is best described by the median.

-The Rome data center is best described by the median. The New York data center is best described by the mean.

Answer 1

To solve this problem, let us first define what is mean and median. Mean is the average of all the numbers in the data set while the median is the number in the middle of the data set in ascending order.

If we create a box plot for the data of Rome and New York, we can see that there is an outlier in the data for New York. Since New York has an outlier, so the mean is not a good representation on the central tendency of the data. The mean is skewed (distorted) by the outlier. So in this case it is better to use the median.

While the Rome data is nice and symmetrical, it does not seem to have an outlier, so we can use the mean for this data set.

Therefore the answer is:

The Rome data center is best described by the mean. The New York data center is best described by the median