Comment by Zenst
4 years ago
I was always bemused that the average family size was 2.4 children as no family fits that average ever. With mode and medium that would not happen.
Of note I have no idea what the average family size is children wise, just going on longstanding data from UK that in itself may be out of date, though does highlight the point.
[EDIT fixed typo]
Yet if we set up a game with a penalty proportional to the distance between your guess and the true number of children for a family, and you guess the median or mode, you'll be right more often than I (because I will never be right), but you will also continually be losing money to my guess of the mean.
What matters in real life is generally not how often you are correct, but rather by how much you are wrong. What you need to minimise is not your error rate, but the consequences when you are wrong. You are free to make an infinite amount of mistakes, as long as you are sure to make them in such a way that they are comparatively insignificant.
> Yet if we set up a game with a penalty proportional to the distance between your guess and the true number of children for a family, and you guess the median or mode, you'll be right more often than I (because I will never be right), but you will also continually be losing money to my guess of the mean.
Not sure were you went there, but the point is that you can overdetail in a way that abstracts from reality.