Several good answers still leave room for more comments.
First, no one has objected to the idea that the median is intended to eliminate outliers, but I will qualify it. The intended meaning is evident, but it is easy for real data to be more complicated. At most, the median is intended to discount or ignore outliers, but even that is not guaranteed. For example, with ratings of 1 1 1 5 5 5 the median and mean agree at 3, so all may seem good. But an extra 5 will tip the median to 5 and an extra 1 will tip the median to 1. The mean would move by about 0.286 in each case. Hence the mean is here more resistant than the median. The example can be dismissed as unusual, but it's not outrageous. The point is not original, naturally. One place it is made is in Mosteller, F. and Tukey, J.W. 1977. Data Analysis and Regression. Reading, MA: Addison-Wesley, pp.34-35.
Second, trimmed means have been mentioned and the idea deserves a bigger push. Mean and median need not be stark alternatives so that the analyst must choose (vote for) one or the other. You can consider all possible trimmed means based on trimming a certain number of values in each tail. The table shows as # the number of values included in the calculation of the mean:
| number # trimmed mean |
| 0 16 4.0625 |
| 1 14 4.214286 |
| 2 12 4.416667 |
| 3 10 4.6 |
| 4 8 4.75 |
| 5 6 4.833333 |
| 6 4 5 |
| 7 2 5 |
The main picture here is that you can choose your discount rate (ignore so many values in each tail as suspect) as a kind of insurance against the risk of being off because of extreme values. What I see is a fairly smooth gradient between mean and median, which is expected here because the possible values 1, 2, 3, 4, 5 are all present in the data. A big jump in the sequence is expected with an isolated outlier.
There is no obligation with trimmed means to trim equal numbers in each tail, but I will not expand on that.
Third, the example is of Amazon reviews. Context is always pertinent in guiding how you want data summarized. In the case of Amazon reviews the best answer is to read the reviews! As high and low grades alike can be on spurious grounds (implicitly: the author of this book is my friend) and/or irrelevant to your decision (explicitly: the re-seller treated me badly), there isn't to me an obvious implication for how to summarize such data, and indeed by showing you the distribution Amazon is being maximally informative.
Fourth, and most elementary but also fundamental of all, who is making you choose? Sometimes mean and median should both be reported (and, as said, a distribution graph too).