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Why You Shouldn’t Trust Statistics

Don’t be fooled by people using the word “average,” particularly when they talk about income. If you’ve ever come across the “average” salary in your state or nation and wondered why you don’t make that much, it’s because some outliers ruin the math by making obscene amounts of money, while there are no outliers in the other direction, since you can’t have “income” at less than zero. This is only one of several comics illustrating how statistics can be manipulated to say anything you want at Math With Bad Drawings. -via Digg  

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I see what you mean. When you say the listener must get the math right, you mean the listener must understand the definitions and implications. Sadly, most people don't even think about it, because numbers are scary and they don't read the real data.

They see headlines that say, for instance, "This type of cancer is up 200%!" when the data says there was one case per million people last year, and three cases per million this year. Totally insignificant in the long run, but makes for sensational headlines.
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As I said, problems happen because either the speaker or the listener is getting the math wrong.If you think a high average starting salary precludes you from getting a low starting salary, you got the math wrong. If you are told an average for a group of people and think that means half of the people got more than average, you got the math wrong, etc.

As you said, the comics have correct math. As such, the statistics were not manipulated and they are not saying anything the speaker wants, but instead are saying a very specific things that happens to be irrelevant to the speaker's point. Many people have this sense that statistics are some sort of vague, wishy-washy un-math that can mean anything. Instead there are very specific, defined meanings, but appear vague because people don't know those definitions and implications.

Learning those meanings, for which comics like these can be very helpful, goes a long way toward seeing the usefulness or uselessness of a massive amount of figures we're bombarded with daily. But saying the statistics can be manipulated to say anything (at least while doing the math correctly) is counterproductive, as if statistics are meaningless which would make learning about them pointless.
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You can't make statistics say anything you want. Problems happen because, either the speaker got the math wrong (on purpose or not), or the listener is getting the math wrong. Learning some basic statistics eliminates the latter, leaving you with just lies and computation mistakes to worry about.
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