# Can I exclude outliers when calculating mean or standard deviation (small-sample)?

I am analyzing my results for a high-school biology paper. My data set consists of 20 groups in total, each having 4 repeats, so each is a small sample. I have a few (4) outliers that have a value lower than the control group (which is practically impossible and thus certainly the effect of a technical error).

Can I exclude the outliers when calculating the mean value or standard deviation, as they largely affect both parameters?

I am quite green when it comes to statistics, so I would hugely appreciate your help. Many thanks!

• Use box plot: en.wikipedia.org/wiki/Box_plot.
– Mo-
Commented Jul 23, 2020 at 14:24
• If you have access to The American Statistician, the paper "Calibration Guidelines Challenge Outlier Practice" by Finney (2012; volume 60 issue 4; pp 309-314; doi: doi.org/10.1198/000313006X150182) does a fantastic job addressing what you should think about with this question. Although @greg-snow's answer is pretty much perfect IMO, I thought I'd link this paper for anyone who comes across this question. Commented Oct 19, 2022 at 20:53

Sometimes the outliers end up being of more interest than the rest of the data. The discovery of penicillin was from studying the outlier.

Can you verify that the outliers are due to technical problems? If you can show that they are impossible values then you have justification for not including them, or you may find something even more interesting when trying to figure out the unusual values.

The general recommendation these days is to not discard outliers without good, external reasons. If you can throw out any values that you do not like, then you can make the remaining data say anything that you want, which is not good science.

If you still do not like the outliers, but cannot show the errors that caused them then you could analyze the data both with and without outliers and show how similar/different the results are. There are also "robust" methods that are less affected by outliers that you could consider using (though you may need to consult with a statistician for those).

• Thanks for your response. In my case the outliers are comparable to a negative age or distance, so they are practically impossible. In that case, can I exclude them when calculating the mean or SD?
– Alex
Commented Jul 23, 2020 at 14:28
• @Alex, if you can document that the values are impossible, then you can drop them from the analysis (but you should still mention what you did and why). Commented Jul 23, 2020 at 15:01

Excludding outliers is used in setting PAT Limits (PART AVERAGE TESTING) for automotive testing. We want to throw the outlier away (Fail it) when calculating the Upper and Lower PAT limits. The outlier would be logged as a failure and Binned as such. Yes outliers are interesting, but not always necessary to keep in a distribution.

I have not determined how to do this. in Excel yet.

• I am not familiar with automotive testing. Are you saying that if a measurement of a part (or a batch of parts) is outside of a quality control limit then that part does not go further toward sale/production? Commented Oct 19, 2022 at 19:13