Final answer:
For a strongly skewed data set, the median is the preferred measure of central tendency as it is less affected by outliers and extreme values than the mean.
Step-by-step explanation:
When a data set is strongly skewed, choosing to present the median over the mean is often considered to be a better representation of the central tendency of the data. Skewness affects the mean more significantly because it is sensitive to all values in the data set, including outliers and extreme values, which can pull the mean away from the center of the data. On the other hand, the median, which is the middle value when the data is ordered from least to greatest, is more resistant to the effects of skewness and outliers, and thus gives a better representation of the 'typical' value in a skewed distribution.
This is especially useful when we're discussing probability distributions in statistical analysis. For right (positive) skewed data, the median is often less than the mean as the mean is influenced by the high-value tail. Conversely, for left (negative) skewed data, the mean is often less than the median. In symmetrical distributions, the mean and median will coincide, proving they provide similar information about the center.