Which measure of central tendency is most affected by extreme values?

The mean is the measure of central tendency that is most affected by extreme values, also known as outliers. This occurs because the mean is calculated by summing all the values in a dataset and then dividing by the number of values. When there are extreme values in the dataset, they can significantly influence the total sum, thereby altering the calculated mean, often pulling it toward the higher or lower extreme.

In contrast, the median, which is the middle value when the data is arranged in order, is less impacted by outliers. It only depends on the position of values rather than their magnitude, making it a more robust measure in datasets with extreme values. The mode, which represents the most frequently occurring value, is also unaffected by extreme values, as it focuses solely on frequency rather than the actual values themselves. The range, while it measures the difference between the highest and lowest values and can reflect extremes, is not a measure of central tendency in the same context as mean, median, and mode.

Therefore, in situations where extreme values exist, the mean will be skewed more than the median or mode, confirming that it is the most sensitive to such values.