Which of these statistical measures is most affected by extreme values?

The mean is significantly influenced by extreme values, also known as outliers, because it is calculated by summing all values in a dataset and then dividing by the number of values. If an extreme value is added to or removed from the dataset, it can markedly change the total sum and thus alter the mean. For example, in a set of salary data where most values are clustered around $50,000, adding one person's salary of $1,000,000 would shift the mean upward, misrepresenting the typical salary of the group.

In contrast, the median, which represents the middle value when data is sorted, remains stable regardless of extreme values, as it focuses only on the central position of the dataset. The mode, being the most frequently occurring value, does not change unless the frequency of an extreme value surpasses that of the existing modes. The range, which measures the difference between the maximum and minimum values, is also affected by extreme values but not in the same manner as the mean since it only considers two values rather than all data points. Therefore, the mean is the statistical measure most susceptible to being skewed by outliers.