A statistic is said to be resistant if it is not significantly affected by extreme values or outliers in the data set. This means that even when very large or very small values are added or changed, the resistant statistic remains relatively stable and does not change much

. Key points about resistant statistics:

• They show little sensitivity to extreme observations in the data.
• Examples of resistant statistics include the median and the interquartile range (IQR) because these focus on the middle portion of the data and ignore extremes.
• Non-resistant statistics, such as the mean , standard deviation , and range , can be heavily influenced by outliers, causing large changes in their values when extreme data points are present

Illustrative example: Consider a dataset without outliers and then add an extreme value:

• Without outlier, median might be 13; with outlier added, median shifts slightly to 14.
• Mean, however, might jump from around 13.5 to nearly 50 with the same outlier added.

This shows that the median (resistant) barely changes, while the mean (non- resistant) changes drastically

. Why resistance matters: Using resistant statistics is important when data contain outliers or are skewed because they provide a more reliable and representative summary of the data's central tendency or spread without being distorted by extreme values

. In summary, a resistant statistic maintains stability and reliability despite the presence of extreme data points, making it preferable for analyzing real-world data that often include outliers.