When is the median used instead of the mean?

The median is often used instead of the mean particularly in the context of skewed data distributions because it provides a better measure of central tendency in such cases. When data is skewed, one or more extreme values can significantly affect the mean, pulling it in the direction of the skew. This can result in a mean that does not accurately represent the center of the data distribution.

For example, consider a dataset of home prices in a neighborhood where most homes are valued around $300,000 but a few luxurious homes are valued at $1 million or more. The mean price will be elevated due to these high values, making it seem like homes are more expensive on average than they truly are for the majority of homeowners. The median, which is the middle value when the data is ordered, remains unaffected by these outliers and provides a clearer picture of a typical home price in that neighborhood.

In contrast, while normally distributed data may have a mean and median that are similar, using the median in skewed distributions can present a more representative value for the center of the data. Other contexts mentioned, like calculating the mode or dealing with categorical data, do not directly relate to the advantages of using the median over the mean. Thus, the median is especially valuable