What effect do outliers have on the median of a dataset?

The median is a measure of central tendency that represents the middle value of a dataset when the values are arranged in order. One of the key characteristics of the median is its resilience to outliers, which are extreme values that differ significantly from other observations in the dataset.

When an outlier is present, because the median is determined by the position of values rather than their magnitude, only the middle value(s) are considered. Therefore, the presence of outliers does not significantly alter the median. In cases where the dataset is small or where the outlier is particularly influential (e.g., the outlier is close to the median), the median may change slightly; however, this change is often minimal compared to how the mean is affected by outliers.

For example, in a dataset like {1, 2, 3, 4, 100}, the median is 3. If we took out the outlier (100), the median would remain 3, demonstrating the median's stability against extreme values.

Options concerning outliers affecting the median greatly, having no effect at all, or only influencing the upper quartile do not accurately reflect the median's nature. Thus, while it is important to consider how outliers can hint at