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The Magic Cafe Forum Index » » Puzzle me this... » » Check my math (4 Likes) Printer Friendly Version

MeetMagicMike
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How can these two statements both be true?

A) Tigers are more dangerous than wolves because if you see a tiger there is a 49% chance you will be attacked. For wolves it's only 5%

B) Wolves are more dangerous than tigers because last year more people were attacked by wolves than by tigers.

Obviously, wolves can't be both more dangerous and less dangerous than tigers but I do believe the supporting statisticcs given can both be accurate. So which is true?
Magic Mike

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landmark
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A) Voldemort is more dangerous than a swimming pool. If you encounter Voldemort there is a 99% chance you will be obliterated. For encounters with a swimming pool, it's much less.

B) Swimming pools are more dangerous than Voldemort. More people died from swimming pools last year than from Voldemort.

And so on. We might instead want to define the annual danger index as the product of the number of encounters expected in a year by the probability of any single such encounter being fatal.
katarinag
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One animal is more dangerous in a one-on-one interaction.

The other lives closer to populated areas (and there are way, way more of them all over the world) so you’re a whole lot more likely to encounter it.

Different criteria / measures. Which is basically the same point Landmark made.
MeetMagicMike
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Thanks guys. I think this is a good example of how statistical data can be abused.
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ddyment
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This isn't so much an example of the misuse of statistics as it is the misuse of language. The discrepancy arises not because of any mathematical concerns, but because the word "dangerous" is used with two different meanings.

In the first example, it is taken to mean "likely risk of death in an encounter"; in the second it is taken to mean "likely risk of death to an overall population". So it's more an "apples and oranges" problem than one of statistics.
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