For example; The Children Puzzle (from NPR):
I tell you that a couple has two children and that (at least) one of them is a boy. I ask you what is the probability that their other child is a boy. Most people think the answer is 1/2, arguing that it is equally likely that the other child is a boy or a girl. But that's not the right answer for the question I have asked you. Here's why. In terms of order of birth, there are four possibilities for the couple's children: BB, BG, GB, GG. When I tell you that at least one child is a boy, I rule out the possibility GG. That leaves three possibilities: BB, BG, GB. With two of these, the other child is a girl; so the probability of the other child being a girl is 2/3. Leaving the probability of the other child being a boy at 1/3.
Now that is kind of a simple problem, but that is the kind of things that we do. A problem is posed and most of the work is figuring out the problem, a very little bit has to do with the actual calculating.
Who would pay for such a thing? The answer surprises a lot of people -almost any company. Companies (and governments) collect data, large amounts of data. They collect data so that they can answer questions, so that they can make a better profit. Statisticians are hired to answer questions the business has by using the data it collects. Sometimes the questions asked (or the way the data is collected) is so complicated that it could take a week to find an answer, even though the actual analysis of the data might take a couple of minutes once the statistician knows how to handle the question and the data properly.
So that's the low-down on statisticians, we don't count things, and we don't only deal with data either, we answer questions using data. And that sort of job pays quite well. ^_^
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