April 30, 2010Math 132: Foundations of Mathematics Amy Lewis Math Specialist IU1 Center for STEM Education

April 30, 2010Math 132: Foundations of Mathematics Odds The odds in favor of E are Odds in favor of E = P(E) P(not E) The odds against E are Odds against E = P(E) P(not E)

April 30, 2010Math 132: Foundations of Mathematics Odds You are dealt one card from a 52-card deck. –Find the odds in favor of getting a red queen. –Find the odds against getting a red queen. The winner of a raffle will receive a two- year scholarship to the college of his or her choice. If 1000 raffle tickets were sold and you purchased 5 tickets, what are the odds of your winning the scholarship?

April 30, 2010Math 132: Foundations of Mathematics 12.1 Sampling, Frequency Distributions, and Graphs Describe the population whose properties are to be analyzed. Select an appropriate sampling technique. Organize and present data. Identify deceptions in visual displays of data.

April 30, 2010Math 132: Foundations of Mathematics Sampling & Populations A population is the set containing all the people or objects whose properties are to be described and analyzed by the data collector. A sample is a subset or subgroup of the population.

April 30, 2010Math 132: Foundations of Mathematics Sampling & Populations A city government wants to conduct a survey among the city’s homeless to discover their opinions about required residence in city shelters from midnight until 6:00 am. –Describe the population. –A city commissioner suggest obtaining a sample by surveying all of the homeless people at the city’s largest shelter on a Sunday night. Does this seem like a good idea? Explain your answer.

April 30, 2010Math 132: Foundations of Mathematics Random Sampling A random sample is a sample obtained in such a way that every element in the population has an equal chance of being selected for the sample. How can you conduct a random sample? –Is American Idol a good example of a random sample? –How do political polls conduct random samples?

April 30, 2010Math 132: Foundations of Mathematics Random Sampling Suppose we want to know how a large city’s citizens feel about casino gambling. Which of the following would be the most appropriate way to select a random sample? –Randomly survey people who live in the oceanfront condominiums in the city. –Survey the first 200 people whose names appear in the city’s telephone directory. –Randomly select neighborhoods of the city and then randomly survey people within the selected neighborhoods.

April 30, 2010Math 132: Foundations of Mathematics Random Sampling Suppose we want to know how students at WACTC feel about changing the school colors. How could you randomly select 30 students to survey?

April 30, 2010Math 132: Foundations of Mathematics Frequency Distributions A frequency distribution is one way to present collected data. –The first column contains data values –The second column contains the number of times each value occurs. Create a frequency distribution for the data showing final course grades for students in a precalculus course: F, A, B, B, C, C, B, C, A, A, C, C, D, C, B, D, C, C, B, C

April 30, 2010Math 132: Foundations of Mathematics Frequency Distributions What about when we have a class of 40 students with nearly 40 different grades? –Check out the data on page 683. –How can we organize this data onto a reasonably-sized frequency distribution?

April 30, 2010Math 132: Foundations of Mathematics Homework Where do you see frequency distributions used in the real-world? Why are they important? Next Session: Monday, May 3