Final answer:
In a skewed distribution, the mean and median can disagree. One should consider the nature of the data and the presence of outliers when deciding whether to use the mean or median as the measure of central tendency.
Step-by-step explanation:
When the mean and median disagree, it suggests that the data has a skewed distribution. If the distribution is skewed to the left, the mean will be less than the median. On the other hand, if the distribution is skewed to the right, the mean will be greater than the median. One should consider the nature of the data and the presence of outliers when deciding which measure of central tendency to use.
For example, in a dataset where 49 people earn $30,000 and one person earns $5,000,000 per year, the median would be a better measure of the center than the mean because the $5,000,000 is an outlier. The median of $30,000 gives a better representation of the middle of the data.
Overall, the mean is more affected by extreme values or outliers, while the median is less influenced by them. It is important to analyze the distribution and characteristics of the data when choosing between the mean and median as the measure of central tendency.