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An outlier is an observation that appears to be unusual or not well described relative to a simple characterization of a dataset. A discomfiting possibility is that these data come from a different population than the one intended to be studied.

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Should you standardize your variables before or after removing outliers?

It depends on what you exactly need for your use-case, but if you remove outliers after standardizing, the resulting data won't be standardized anymore (if many outliers are removed, standard deviation … could become considerably smaller than 1) So, if you are about to use a procedure where scaled data in needed, you should definitely remove your outliers first, then standardize. …
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1 vote

Check statistical significance of one observation

With only 1 observation, it is quite easy. Look how many standard deviations out of the mean your new data point is (this is, subtract the "data" mean and divide by the "data" standard deviation) Now …
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