Which measure is NOT robust regarding extreme values?

The mean is not robust regarding extreme values because it is calculated by adding all the values in a dataset and dividing by the number of observations. This means that even a single extreme value, or outlier, can significantly affect the mean, pulling it in the direction of that outlier. For instance, if you have a dataset that generally ranges around a small number and includes one very large outlier, the mean will be skewed toward that outlier, misrepresenting the central tendency of the rest of the data.

In contrast, measures like the median and the interquartile range (IQR) are more resistant to the influence of extreme values. The median is the middle value when the data is sorted, meaning that it only considers the central point and is unaffected by how extreme the outer values are. The IQR measures the spread of the middle 50% of data and, therefore, similarly remains largely unchanged by extreme values. The mode, being the most frequently occurring value, also does not get impacted by outliers in the same way that the mean does.

Therefore, the mean is the measure that is least robust in the presence of extreme values.