Why is the median less affected by extremely large or small values than the mean?
Swiss commemorative stamp of mathematician Jakob Bernoulli, issued 1994, displaying the formula and the graph for the law of large numbers, first proved by Bernoulli in 1713.
In statistics, the mean is calculated by summing all data points and dividing by the total count, meaning every value in the set directly influences the result. Because the mean accounts for the magnitude of every observation, extremely large or small valuesâoften called outliersâcan pull the average toward them, potentially misrepresenting the "typical" value of the dataset.
In contrast, the median is a positional measure defined as the 50th percentile, or the middle value of an ordered dataset. Its value is determined by the relative order of the data points rather than their specific numerical magnitudes. Because the median only considers the center of the distribution, it remains stable even if the extreme values at the ends of the set are changed significantly. This property makes the median a more robust measure of central tendency when dealing with skewed data or datasets containing extreme outliers.1