Which of the following measures is considered robust against outliers?

The median is considered a robust measure of central tendency because it is not significantly affected by outliers or extreme values in the data set. When calculating the median, one arranges the data in ascending order and selects the middle value (or the average of the two middle values if there is an even number of observations). This process focuses purely on the central position of the data and ignores the magnitude of the values themselves, allowing the median to provide a better representation of the data's center in the presence of outliers.

In contrast, the mean, standard deviation, and range are sensitive to extreme values. For example, the mean takes into account every value in the dataset, and a few extremely high or low values can skew the average significantly. The standard deviation, which measures the dispersion of data points around the mean, is also influenced by outliers because it is based on the squared differences from the mean. The range, defined as the difference between the maximum and minimum values, would also be greatly affected by outliers, as a single extreme value can expand the range significantly. Thus, the median is preferred in datasets where outliers are present, making it the best choice when looking for a robust measure.