Which measure of central tendency is most affected by outliers in a small sample set?

The mean is the measure of central tendency that is most affected by outliers in a small sample set. This is because the mean is calculated by summing all the values in the dataset and then dividing that sum by the number of values. Therefore, if there is an extremely high or low value within the dataset (an outlier), it can significantly skew the mean, pulling it upwards or downwards depending on the direction of the outlier.

In contrast, the median, which represents the middle value when the data is ordered, remains stable regardless of extreme values that appear in the dataset. Similarly, the mode, which is the value that occurs most frequently, is unaffected by outliers because it only concerns the frequency of values rather than their magnitude. The range, while indicating the span of the data by subtracting the minimum value from the maximum, is also influenced by outliers but is not a measure of central tendency.

Thus, the mean's sensitivity to extreme observations makes it particularly susceptible to being distorted when there are outliers present, especially in smaller sample sizes where each value holds greater weight in the overall calculation.