Resistant Statistic — Definition, Formula & Examples
A resistant statistic is a summary measure that is not significantly changed by outliers or extreme observations in a data set. The median and IQR are resistant; the mean, standard deviation, and range are not.
A statistic is called resistant (or robust) if its value is relatively unaffected by changes in a small proportion of the data, particularly by the addition or removal of extreme values. Formally, a statistic resists the influence of outliers on its computed value.
How It Works
To determine whether a statistic is resistant, consider what happens when you replace a typical data value with an extremely large or small one. If the statistic barely changes, it is resistant. The median is resistant because it depends only on the middle position of sorted data, not on the actual magnitude of extreme values. The mean is non-resistant because every value contributes directly to the sum, so a single outlier can drag the mean far from the center of the distribution.
Worked Example
Problem: Consider the data set: 10, 12, 14, 15, 16. Now change the last value to 500, giving 10, 12, 14, 15, 500. Compare the mean and median before and after.
Original mean: Add all five values and divide by 5.
New mean: Replace 16 with 500 and recalculate.
Compare medians: In both data sets the middle value (third of five) is 14. The median stays at 14 regardless of the outlier.
Answer: The mean shifted from 13.4 to 110.2 — a massive change — while the median remained 14. This demonstrates that the median is a resistant statistic and the mean is not.
Why It Matters
On the AP Statistics exam, you are frequently asked to justify choosing the median over the mean for skewed distributions. Understanding resistance helps you make that argument correctly. In real-world data — salaries, home prices, medical costs — outliers are common, so analysts routinely report resistant statistics to give a more representative summary.
Common Mistakes
Mistake: Assuming the mode is always resistant.
Correction: The mode depends on frequency counts, not position or magnitude, so it is technically unaffected by outliers. However, the AP exam focuses on median and IQR as the standard resistant measures of center and spread. Don't confuse resistance with simply being unrelated to extreme values.