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Inferential statistics, is used to make claims about the populations that give rise to the data we collect. This requires that we go beyond the data available to us. Consequently, the claims we make about populations are always subject to error; hence the term "inferential statistics" and not deductive statistics.
An extra credit idea for AP Statistics which benefits the whole class is students researching a specific concept and presenting the concept to the class.
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.
There are two types of statistics. One is called descriptive statistics and the other is inferential statistics. Descriptive statistics is when you use numbers. Inferential statistics is when you draw conclusions or make predictions.
Psychological statistics is the application of statistics to psychology.