Which of these measures 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 is because the mean is calculated by summing all the values in a dataset and then dividing that sum by the number of values. Therefore, if an extreme value is present in the dataset, it can significantly shift the average upwards or downwards, making it less representative of the typical values in the dataset.

In contrast, the median, which is the middle value when the data is sorted, remains unchanged regardless of how extreme the outliers are, as long as the outlier does not alter the overall order of the data. The mode, being the most frequently occurring value, is also unaffected by extreme values, since it solely depends on the frequency of occurrences. The range reflects the difference between the maximum and minimum values and is influenced by the extreme values; however, it does not provide a central tendency measure like the mean, median, or mode. Thus, the mean is uniquely susceptible to being skewed by extreme values, making it the correct choice in this context.