### 3.3 Deductive & Inductive Reasoning

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• Math Help

If you take a course in statistics, you will learn that statistical inference is almost always based on inductive reasoning. The only cases in which this is not true are when you are able to sample an entire population.

In most cases, the sample taken is small compared to the population, and the inference is stated with a degree of uncertainty. For instance, you might say, "I am 95% certain that the mean height of men in the United States is 70 inches, plus or minus 1 inch."

The point is that inductive reasoning does not generally provide us with certainty. And yet, as humans, we are all comfortable living with uncertainty. It exists, often unsaid but understood, in almost all of our conversations.

For instance, when you tell someone, "I'll be there in about 10 minutes," both you and the person listening to you understand that something could happen to make the statement false.

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• Pollution

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One can hardly pick up a newspaper or news magazine without reading about other examples of inductive reasoning related to environmental issues. Here are a few examples.

• Overpopulation by humans, which many environmentalists agree is the primary problem.
• Global warming, which is a result of overpopulation.
• Indirect threatening of animal species by destruction of habitat.
• Direct threatening of animal species by fishing and hunting.
• Poisoning of the environment through garbage, plastics, and toxic waste.

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