A statistic is said to be resistant if it is not sensitive to extreme values.
Two examples of statistics that are resistant include:
- The median
- The interquartile range
Examples of statistics that are not resistant include:
- The mean
- The standard deviation
- The range
The following example illustrates the difference between resistant and non-resistant statistics.
Example: Resistant vs. Non-Resistant Statistics
Suppose we have the following dataset:
Dataset: 2, 5, 6, 7, 8, 13, 15, 18, 22, 24, 29
Using a calculator or statistical software, we can compute the value of the following resistant statistics for this dataset:
- Median: 13
- Interquartile range: 13.5
We can also compute the value of the following non-resistant statistics for this dataset:
- Mean: 13.54
- Standard deviation: 8.82
- Range: 27
Now consider if this dataset had one extreme outlier added to it:
Dataset: 2, 5, 6, 7, 8, 13, 15, 18, 22, 24, 29, 450
We can once again compute the value of the following resistant statistics for this dataset:
- Median: 14
- Interquartile range: 15.75
We can also compute the value of the following non-resistant statistics for this dataset:
- Mean: 49.92
- Standard deviation: 126.27
- Range: 448
Notice how drastically the non-resistant statistics changed by simply adding one extreme value to the dataset:
Conversely, the resistant statistics barely changed at all. Both the median and the interquartile range only changed by a little.
When to Use Resistant Statistics
The most common statistics used to measure the center and the dispersion of values in a dataset are the mean and the standard deviation, respectively.
Unfortunately, these two statistics are sensitive to extreme values. So, if outliers are present in a dataset then the mean and standard deviation won’t accurately describe the distribution of values in a dataset.
Instead, it’s recommended to use the median and the interquartile range to measure the center and the dispersion of values in a dataset if outliers are present because these two statistics are resistant.
Additional Resources
How Do Outliers Affect the Mean?
When to Use Mean vs. Median
When to Use Interquartile Range vs. Standard Deviation