Subjective Type

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

Solution

Explanation:
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 statistic).

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 in 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 extrreme), the mean increases to 97.55, $$ s \approx 299.33, $$ and $$ \sigma $$ increases to $$ \sigma \approx 285.40. $$

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

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