Which measure of central tendency is most affected by outliers?

The mean is the measure of central tendency that is most affected by outliers because it is calculated by summing all values in a dataset and dividing by the total number of values. When an outlier is present, it can significantly alter the sum of the data, thus skewing the mean in the direction of the outlier. For instance, in a dataset of exam scores where most scores are in the range of 70 to 90, a single score of 5 or 100 can pull the mean much lower or higher than the rest of the data, misrepresenting the central location of the majority of values.

In contrast, the median, which is the middle value in an ordered dataset, remains unaffected by extreme values since it only depends on the position of the data rather than the actual values themselves. The mode, the value that appears most frequently, also does not change based on outliers unless the outlier takes on the value that is already the most common. Variance measures the spread of a dataset and is influenced by all values but does not quantify central tendency in the same way. Thus, the mean is the most sensitive and is greatly impacted by the presence of outliers.