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

• 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 and 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.