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AP STATISTICS LESSON 6 - 1

AP STATISTICS LESSON 6 - 1. THE IDEA OF PROBABILITY. ESSENTIAL QUESTION: How is probability used in Statistics?. Objectives: To develop a working understanding of Probability. To understand what is meant by “Random,” and what it’s characteristics are in the long run. Introduction.

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AP STATISTICS LESSON 6 - 1

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  1. AP STATISTICSLESSON 6 - 1 THE IDEA OF PROBABILITY

  2. ESSENTIAL QUESTION: How is probability used in Statistics? Objectives: • To develop a working understanding of Probability. • To understand what is meant by “Random,” and what it’s characteristics are in the long run.

  3. Introduction Probability is a branch of mathematics that describes the pattern of chance outcomes. The reasoning of statistical inference rests on asking, “ How often would this method give a correct answer if I used it many, many times?”

  4. The Idea of Probability • Probability begins with the observed fact that some phenomena are random – that is , the relative frequencies of their outcomes seem to settle down to fixed values in the long run. • The big idea is this: chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run. • The tossing of a coin can not be predicted in just a few flips, but there is a regular pattern in the results, a pattern that emerges clearly only after many repetitions.

  5. Example 6.1 Page 331 COIN TOSSING For the first few tosses the proportion of heads fluctuates quite a bit, but settles down as we make more and more tosses.

  6. Randomness and Probability Randomness in statistics is not a synonym for “haphazard” but a description of a kind of order that emerges only in the long run. The idea of probability is empirical. That is, it is based on observation rather than theorizing.

  7. Randomness and Probability(definitions) • We call a phenomenon random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions. • The probability of any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions. That is, probability is long – term relative frequency.

  8. Thinking about Randomness • That some things are random is an observed fact about the world. • Independent – The outcome of one trial must not influence the outcome of any other.

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