One reason the median and mean are often reported together as measures of central tendency is that the median is not nearly as sensitive to outliers as the arithmetic mean. From the fact that a dataset (like Petersen’s contributions) has a mean of $334 but a median of $100 you can tell there are outliers on the high side included in that data set.

Reporting both measures of central tendency using all the data is, I think, a better strategy than selectively eliminating data and then computing whatever “average” seems appropriate.

On a related point, note that there are several outliers on the low end in Taylor’s dataset. Why anyone contributes $1 to a political campaign is beyond me, but the effect of that contribution is to drive down the arithmetic mean. Same with the several $5 donations – which Taylor’s campaign on at least one occasion (after close of books, however) explicitly solicited in that amount. Do you say, “Oh, well, that’s not a legitimate donation for my analysis, so I’ll just eliminate it.”? My answer is no.