*7*

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 wonâ€™t accurately describe the distribution of values in a dataset.

Instead, itâ€™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