Which measure of spread is most sensitive to extreme values?

The standard deviation is the measure of spread that is most sensitive to extreme values, often referred to as outliers. This sensitivity arises from the fact that standard deviation is calculated using the mean of the data set. When extreme values are present, they can significantly influence the mean, leading to a larger standard deviation. The formula for standard deviation squares the differences between each data point and the mean, which not only emphasizes larger deviations but also causes even a single extreme value to have a disproportionately large impact on the overall calculation.

In contrast, median, range, and interquartile range are less affected by extreme values. The median is based solely on the middle value of a data set, and thus remains stable even if outliers are present. The range, which measures the difference between the maximum and minimum values, can be affected by outliers but does not account for the distribution of the values in between. The interquartile range focuses on the middle 50% of data, essentially ignoring the lowest and highest quartiles, and is therefore shielded from extreme values.

Thus, standard deviation's reliance on the mean and the squaring of deviations explains why it is the most sensitive to extreme values, making it the correct choice in this context.