# Is the sample standard deviation "s" a resistant measure?

Aug 3, 2015

I'm not a statistician, but my understanding is that measures of dispersion can be resistant to outliers or not, as well as measures of central tendency (any descriptive statistic can be resistant or not). Moreover, $s$ is not a resistant measure (whereas, the interquartile range, for instance, is).

#### Explanation:

I think the distinction between population standard deviation and sample standard deviation is irrelevant for this question. We could be talking about either kind ($s$ or $\sigma$) as a descriptive statistic of a data set and it would not be resistant (there's no need to get into inferential statistics).

Just take an example data set.: 2, 7, 4, 3, 14, 5, 8, 11, 13, 9, 11

The mean is about 7.91, $s \approx 4.085$, and $\sigma \approx 3.895$ (whether this is sample data or population data depends on the context). The first quartile is 4, the median is 8, and the third quartile is 11. The interquartile range is $11 - 4 = 7$.

If we decide to increase the biggest number, 14, to 1000 (let's go ahead and be extreme), the mean increases to 97.55, $s$ increases to $s \approx 299.33$, and $\sigma$ increases to $\sigma \approx 285.40$.

On the other hand, the first quartile, median, third quartile, and interquartile range are unaffected.