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I have data that do not follow a normal distribution. The data looks like: skewed data.

Can I calculate mean and median with such non-normal distributed data?

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Yes, you can. The mean and median are purely descriptive and can be calculated for any sample, and they always have the same interpretation.

What you cannot do is calculate quantiles based on normal distribution assumptions, as in "95% of the data lie between the mean plus/minus two standard deviations".

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