More vague questions about statistics

  1. What qualities of a situation make statistics appropriate or useful?
  2. Basic statistics makes a lot of assumptions that have to be wrong (charitably: not exactly right), so how does it manage to work much of the time anyway? Things like: Stationarity, possibly independence.
  3. How does the question of "what counts as" interplay with the meaningfulness of statistics?
  4. If statistics didn't work at all, how would you know?
  5. Sometimes a model or a way of counting is slightly wrong; what practical moves do people do to make them right?