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# Collecting Data: Surveys, Experiments, Observational Studies for AP Statistics (page 2)

based on 2 ratings
By McGraw-Hill Professional
Updated on Feb 3, 2011

### Random Variables

A random variable can be thought of as a numerical outcome of a random phenomenon or an experiment. As an example of a discrete random variable, we can toss three fair coins, and let X be the count of heads; we then note that X can take on the values 0, 1, 2, or 3. An example of a continuous random variable might be the number of centimeters a child grows from age 5 to age 6.

An understanding of random variables is what will allow us to use our knowledge of probability in statistical inference. Random variables give rise to probability distributions (a way of matching outcomes with their probabilities of success), which in turn give rise to our ability to make probabilistic statements about sampling distributions (distributions of sample statistics such as means and proportions). This language, in turn, allows us to talk about the probability of a given sample being as different from expected as it is. This is the basis for inference. All of this will be examined in detail later in this book, but it's important to remember that random variables are the foundation for inferential statistics.

There are a number of definitions in statistics. Although you may not be asked specific definitions on the AP Exam, you are expected to have the working vocabulary needed to understand any statistical situation you might be presented with. In other words, you need to know and understand the vocabulary presented in the course in order to do your best on the AP Exam.

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