Which measure of central tendency is best used when data includes extreme values?

The median is the best measure of central tendency to use when data includes extreme values, commonly referred to as outliers. This is because the median represents the middle value of a dataset when it is ordered, effectively dividing the dataset into two equal halves. When extreme values are present, they can skew the mean significantly, making it less representative of the typical value in the dataset.

For example, in a set of numbers where most values are clustered around a particular point but there are a couple of very high or very low values (such as income data where most individuals earn between $40,000 and $60,000, but one person earns $1,000,000), the mean income would be heavily influenced by the extremely high income, resulting in a figure that does not accurately represent the majority of the population. In contrast, the median would remain stable, reflecting the center of the actual distribution of most of the values.

This makes the median particularly valuable in scenarios with skewed distributions or when the data includes outliers, allowing for a more accurate understanding of the central tendency without being misled by extreme values. Such resilience to distortion by outliers is what makes the median the preferred choice in these contexts.