One subject they're important in is physics. Statistics play such a big role in thermal dynamics that it is often referred to as statistical mechanics. Also, probability theory uses statistics as its base and quantum mechanics is all about probability.
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The relevance of political science to statistics and logic is that it helps politicians use the statistics collected to think logically about what their subjects need.
Because they enjoy studing those subjects.
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For example, if you are developing a drug, you try it out on test subjects. Statistics can help you figure out if the drug is effective in treating a condition or if the drug is dangerous.