A few interesting statistical facts

1. This one has gotten a lot of press recently, so it’s not so new; so bear with me if you’ve heard before:

For almost everyone, your friends have more friends than you do.

It remains true if instead of friends you substitute most other types of contacts: most of the people you follow on twitter have more followers than you do.

(The fact that most of your sexual partners had more sexual partners than you had is another reason to practice safe sex.)

2. I don’t know if this one has a name, but it’s about full busses, so we can call it the bus paradox: most people ride in busses that are fuller than average.

Let’s say that there are two types of bus: 25% of busses are completely full, the other 75% are empty (except for the driver). Then, riders will always experience full busses even if most busses are empty. This is true even if only 1% of busses are full, but the 25% number is a bit closer to reality. During rush hour, half the busses are very full (those going into town in the morning; out of town in the evening), even though the typical bus is pretty empty.

It comes up in other contexts, of course: restaurants are on average emptier than is experienced by the typical patron. It can even have public policy implications: the expensive publicly-funded football stadium is less used than the typical visitor realizes (“everytime I go there, it’s full, so it must have been a good investment” is wrong).

3. (This one is true in some countries in Europe): Most families only have a single child, but most children have siblings.

This is a variation on the bus paradox above. Let’s say 66% of families have 1 child, and 34% of families have more than 1. Then, most of the children are coming from that 34% of families with many children (at least 68 for every 66 single children, probably more) and they’ll have siblings.

Larger families are over-represented in the next cohort (in a country with a 1.2~1.3 birthrate, a family of 5 is four times over represented in the younger cohort).

What all of these have in common is that the fact that you are an observer makes you biased. They also remind us that it is a mistake to generalize too much from our own experience as the fact that we are observing something can itself be a confounding effect.

3 thoughts on “A few interesting statistical facts

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