Should we identify outliers from population prior to taking sample? I am revising undergrad statistics course via this course, where i am learning technique to pull out sample from population.
While ensuring that sample is decent representative of population, i am left with this couple of question.


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*Should we care about identification and rectification of outliers prior to taking sample from population ?


Here is my work from where i came up with this question
 A: This depends hugely of what you even want to do about outliers, through what mechanism they arise and whether they even affect what you want to do.
If outliers are perfectly good values that just happen to be (a bit) extreme, then it may be more a matter of making sure it does not affect what you intend to do too much. Some statistical procedures/summary measures are inherently more robust in this respect, while other have more problems. 


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*E.g. if you want to find the population median of something, outliers do not really matter much. 

*On the other hand, a mean might be much more heavily affected, e.g. if you are trying to find the mean of a log-normal distribution, directly taking the sample mean may be a bad idea, if you have just a few values. On the other hand, estimating the parameters of the distribution and then obtaining the theoretical mean from that would likely work a lot better.


If outliers arise through a corrupted sampling process (e.g. people deliberately give nonsense answers to a questionnaire, some biological sample was accidentally contaminated with some other substance etc.), you probably do indeed want to do something about those values. However, what you do depends on what you assume the process that creates these corrupted values to be (following the terminology of missing completely at random/at random/not at random for missing data): 


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*Is it "completely at random" (it might be a reasonable assumption that whether or not a lab technician spoilt a biological sample had nothing to do with what you would have measured on this sample)?

*Is it "at random" (perhaps young people are more likely to give nonsense answers to questions, but their true response would otherwise have been distributed like for other young people)?

*Or is it "not at random" (e.g. people are reluctant to given answer A and rather give a nonsense answer instead, or the lab technician accidentally spoilt the biological sample, because she was shocked by how many bacteria she saw etc.)?

A: In general, you won't have the population. So, if you, in class exercises, remove the outliers from the population before taking the sample, your exercises will be poor examples for the students when they do future work.
