[brey]

  Looking at repeat donations prompted us to ask: do people donate more or less 
  their second time? On average, the answer is roughly 50% more. While first 
  donations had a mean of $88 and a median of *$30*, repeat donations had a mean 
  of $114 and a median of *$50*.

  Average doesn’t mean typical, however. If you look at each repeat donor one by one, 
  it turns out they’re split almost exactly into thirds: 33% donate less the second time 
  (most commonly half), 35% donate more (most commonly double), and 32% donate 
  exactly the same. The averages get pushed up because doubling (and the 
  occasional tripling or even quadrupling) makes a bigger difference overall 
  than halving does.

that's odd. wouldn't you expect the median to stay about the same if 1/3 donated less, 1/3 donated the same, and 1/3 donated more?

[brey]

ah, no, I was wrong - the median only stays the same if only people in the lower half beforehand gave less, and only people in the upper half gave more.

if people cross the old median, this is perfectly possible. although initially counter-intuitive ...

[corin_]

Not just if they cross the median, the median might cross them - for example what if the only people to come back to donate a second time were above the median in their first donation, then even if they all donated the same amount the second time, the median of second-donations would still go up.