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 (outliers) because it is calculated by summing all the values in a dataset and dividing by the number of values. This means that if there are any particularly high or low values, they will have a significant impact on the overall average. For instance, if a dataset contains most values around 10, but one value is 100, the mean will be skewed upward, misrepresenting the typical value in the dataset.

In contrast, the median, which is the middle value when the data is ordered, remains stable even in the presence of outliers, as it only depends on the position of the values rather than their actual magnitudes. The mode, being the most frequently occurring value, is also unaffected by outliers since it is based on frequency rather than numerical calculation. The range, which measures the difference between the maximum and minimum values in the dataset, is influenced by extremes but does not represent a central tendency measure in the same way the mean does.

Thus, the mean is the most affected by extreme values, making it the correct choice in this context.