Final answer:
The mean and median are the two measures of center commonly used. The median is better for datasets with extreme values or outliers, while the mean takes into account the exact values of all data points. The choice between the two measures depends on the characteristics of the dataset.
Step-by-step explanation:
The debate between Tau and Ian regarding the best measure of center for a dataset involves understanding the characteristics of mean and median. The mean is calculated by adding up all the values in the dataset and then dividing by the total number of values. The median, on the other hand, is the middle value when the dataset is arranged in ascending or descending order.
In a dataset where there are extreme values or outliers, the median is generally a better measure of center because it is not affected by these extreme values. This is because the median only considers the position of the values, not their actual numerical values. However, the mean is the most commonly used measure of center in practice. It takes into account the exact values of all the data points in the dataset.
To create a dataset where either the median or mean is the most suitable measure of center, we can consider an example. Let's say we have a dataset of students' test scores. If the scores are fairly distributed and there are no extreme values, the mean would be an appropriate measure of center. However, if there are a few students with very high or very low scores that do not represent the overall performance of the majority, the median would be a more suitable measure of center.