Your arrival at the bus stop, the time you inspect is likely to be at a longer time interval than a shorter

Let's say that a bus comes every 10mins. Even if there's a slight variation from the scheduled arrival of a bus, the average waiting time will be more than 5 minutes.

A common example is the apparent paradox of class sizes. Suppose you ask college students how big their classes are and average the responses. The result might be 56. But if you ask the school for the average class size, they might say 31. It sounds like someone is lying, but they could both be right. The problem is that when you survey students, you oversample large classes. If there are 10 students in a class, you have 10 chances to sample that class. If there are 100 students, you have 100 chances. In general, if the class size is x, it will be overrepresented in the sample by a factor of x.

The same effect applies to passenger planes. Airlines complain that they are losing money because so many flights are nearly empty. At the same time passengers complain that flying is miserable because planes are too full. They could both be right. When a flight is nearly empty, only a few passengers enjoy the extra space. But when a flight is full, many passengers feel the crunch. Once you notice the inspection paradox, you see it everywhere. Does it seem like you can never get a taxi when you need one? Part of the problem is that when there is a surplus of taxis, only a few customers enjoy it. When there is a shortage, many people feel the pain.

Another example happens when you are waiting for public transportation. Buses and trains are supposed to arrive at constant intervals, but in practice some intervals are longer than others. With your luck, you might think you are more likely to arrive during a long interval. It turns out you are right: a random arrival is more likely to fall in a long interval because, well, it’s longer.

Τι στατιστικό πρόβλημα υπάρχει εδώ; 😃