Final answer:
Without complete information on skewness or outliers, we cannot definitively decide whether Tau's preference for the median or Ian's preference for the mean is the correct measure of center. However, the median is typically more reliable in skewed data or when outliers are present.
Step-by-step explanation:
To determine whether Tau or Ian has the better answer, we need to first consider the characteristics of the data presented (23, 24, 13, 16, 23, 24, 23, 22, 12, 23, 20, 23). We should examine whether the data is skewed and whether there are outliers that might affect the mean. Measures of the center, such as mean, median, and mode, give us different insights about data. The mean is the arithmetic average and can be influenced by extreme values, the median represents the middle value when data is ordered, and the mode is the most frequent value.
According to section 2.5 on Measures of the Center of the Data, the median is a better measure when data contains outliers or is skewed because it is less affected by extreme values. If the data is symmetrical, the mean and median will be close or the same, however, when data is skewed, the mean tends to reflect this by being greater or lesser than the median, being pulled in the direction of the skew.
In this case, if we find the data is skewed, Tau would be correct to suggest that the median is a better measure of center. However, we're not provided with enough information in the question to definitively determine the skewness of the data set. Furthermore, the question references another example stating the mean is affected the most by skewing, which suggests that if this data set had a similar skew, Tau might be more accurate.