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I am currently dealing with data with many outliers and I shall not to eliminate them from the data for analytical purposes. What measure shall I use to describe central tendency of the data yet with a less sensitive measure than the mean?

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Median, subsample mean, RPCA, any robust statistic operator...

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The median is a smart choice here since it is pretty robust against outliers. It represents the value which splits the data between the lower half and the higher half - it can be read as the 50% percentile.

https://en.wikipedia.org/wiki/Median

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