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I am not able to distinguish outliers: when to go with the std. dev. or when we need to go with the median.

My understanding on std. dev. is: if the data point is away from the mean by more than 2 std. dev., we consider that as an outlier. Similarly for the median, we say that any data point that is not in-between Q1 and Q3 is an outlier.

So I am confused as to which one to choose.

Can you guys help me understand?

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  • $\begingroup$ Some of the trouble is that outlier detection, particularly when it comes to removing points, isn’t taken so seriously by statisticians: statmodeling.stat.columbia.edu/2014/06/02/…. (The link says it’s about stepwise regression, but it addresses outlier detection, too.) If you have a data point that does not fit your model, perhaps consider changing the model, not changing the data (reality). // I’ve never heard anyone else call points below Q1 and above Q3 outliers. That makes half of the observations outliers. $\endgroup$
    – Dave
    Aug 19, 2021 at 10:27

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It completely depends on the context of the data that is being considered. For example, $2\sigma$ from the mean ($\mu$), depends on the distribution of the data. What is the value of $\mathbb{P}(-2\sigma < X - \mu <2\sigma)$.

Also, there are many methods for outlier detection, and all of them depend on the context. Hence, you cannot say which method should be used by taking it outside the context. You should do some experiments by these methods over the data, and then base on the real outliers sample, decide which method is proper for the current data.

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  • $\begingroup$ I understand that it depends on the context of the data but not sure on how to relate What should be used when? . I think if you can give a a real-time scenario , it would help. $\endgroup$
    – exp post
    Nov 20, 2019 at 4:12

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