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In order to establish an overall rating for a product from a series of user ratings (from 1 to 5), I thought that the median would be a good idea so that extreme values would not have too much influence. But in doing so, it is hard to rank products since they will all have a whole ranking.

So I thought about averaging the mean and the median. Is this a known measure? Is it relevant in this case?

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  • $\begingroup$ What kinds of situations do you find problematic? Something like a product with a single five-star rating outranking a product with 99 five-star ratings and a single four-star? If so, using the median won't help much, but you should instead consider additive smoothing. $\endgroup$ – Ilmari Karonen Sep 20 at 17:41
  • $\begingroup$ Rather the case where a group of people start putting 0's, their impact will be reduced with the median, it's as if they put just below the product score, not a zero. $\endgroup$ – Gulliver Sep 21 at 8:19
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No, it sounds like an odd metric. I suspect the parametric distributions often calculable for the median and mean would be rather nasty for the average of the two which would make this unpopular among statisticians.

I suspect you mean "outliers" by extreme values. If you consider the definition of an outlier:

In statistics, an outlier is a data point that differs significantly from other observations.

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

(I checked a few definitions and most of them are like this).

I think on a discrete scale of 1 to 5, the idea of an outlier sounds odd. As you can see "differs significantly" is open to interpretation and I don't think 1 or 5 differ greatly from 2-4 unless the rest of your user ratings are at 3 only.

In any case, it is probably best to just use the mean. If you lack the variation in the data to seperate out the objects you want using the mean +- std dev or confidence intervals then that's just the data and there's not much you can do about it.

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