HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Chapter 1 Statistics and Problem Solving

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. HAWKES LEARNING SYSTEMS math courseware specialists Learn the basic vocabulary of statistics. Distinguish between populations and samples. Distinguish between parameters and statistics. Statistics and Problem Solving Sections Getting Started Objectives:

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Statistical forecasts based on sample estimates are becoming increasingly accurate. The table to the right shows the predicted percentages of the popular vote for the winning candidate prior to the election and the actual percentage of the popular vote received by the candidate. Presidential Polls YearCandidates Winners Predicted % Actual Winning % Deviation 1984 Reagan Mondale 59%59.2%−0.2% 1988 Bush Dukakis 56%53.0%+3.0% 1992 Clinton Bush Perot 49.0%43.3%+5.7% 1996 Clinton Dole Perot 52%49.2%+2.8% 2000 Bush Gore Nader 48%47.9%+0.1% 2004 Bush Kerry % −1.7% 2008 Obama McCain 55%53.0%+2.0% Who Will Be Our Next President?

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. What Methods do Statisticians Use to Make Predictions? Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Populations Frames Population Parameters Samples Sample Statistics

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Statistics and Problem Solving 1.1 Who will be the next president? Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Definition: In statistics the group we wish to study is called the population. A population is: Defined by what the researcher is studying. The total number of subjects or things we are interested in studying. Populations are of considerable interest to presidential candidates. In the world of political science this “data-driven” approach is called populism.

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Statistics and Problem Solving 1.1 Who will be the next president? If someone is studying monkeys in Brazil, all the monkeys in Brazil would constitute the population. If you are studying students at your college, then all the students attending your college represent a population. Citizens who are registered to vote in a presidential election constitute a population of considerable interest to presidential candidates. Can you think of any examples of populations? Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Examples of Populations:

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Statistics and Problem Solving 1.1 Who will be the next president? Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Definition: In statistics a frame is a list containing all members of the population. Frames are easier developed for smaller populations. A strict definition of census is a survey that includes all elements or units in the frame.

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Statistics and Problem Solving 1.1 Who will be the next president? Can you think of any examples of frames? Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Examples of Frames: The frame for the population of the U.S. would be a rather long list containing about 290 million names. If your statistics class were the population under consideration, the class roll would be the frame. For the population of registered voters, the electoral register would be the frame.

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Statistics and Problem Solving 1.2 Statistics and Quality Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Definition: Population parameters are facts about the population. Parameters are descriptions of the population. A population can have many parameters. Parameters can be in the form of percentages, maximums, minimums, or other characteristics.

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Statistics and Problem Solving 1.2 Statistics and Quality Population Parameters: For a presidential election, some population parameters in which candidates and pollsters are interested in are: The percentage of eligible voters who will vote on Election Day. The percentage of voters who will vote for a specific candidate. The percentage of men/women who favor a candidate. The percentage of people who favor a candidate. The average income of the voters who favor a candidate. Statistics and Problem Solving Section 1.1 Who Will Be Our Next President?

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Can you think of any examples of population parameters? Statistics and Problem Solving 1.2 Statistics and Quality Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Examples of Population Parameters: 67% of Americans 20 and over are overweight. 7 out of 10 Americans do not exercise regularly. 70 million Americans suffer from a sleep disorder.

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Statistics and Problem Solving 1.2 Statistics and Quality Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Definition: A sample is a subset of the population which is used to gain insight about the population. Samples are used to represent a larger group, the population. For example, the percentage of votes a presidential candidate received on Election Day is a parameter. Sample data is used to try to estimate this population parameter. Another example is sampling a college campus to represent the population of college students in the U.S.

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example: PopulationAmericans SampleAll college students Statistics67% are sleep deprived 25% combat stress with exercise For any given sample a statistic is a fixed number. Because there are lots of different samples that can be drawn from the population, statistics vary depending on the sample collected. Statistics are used as estimates of population parameters. Statistics and Problem Solving 1.2 Statistics and Quality Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Definition: A statistic is a fact or characteristic about a sample.

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Collect Data Defines Population/ Variables Question Calculate Statistic Estimate Parameter Statistics and Problem Solving 1.2 Statistics and Quality Statistics and Problem Solving Section 1.1 Who Will Be Our Next President?

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Statistics and Problem Solving 1.2 Statistics and Quality Definition: A process is a method for obtaining a desired result. For a physician, a process is a treatment performed in a series of steps designed to improve a patient’s condition. In business, a process is a series of steps that produces a product or service. Statistical Process Control (SPC) is a group of statistical methods designed to monitor and control processes. SPC is also helpful in detecting problems in a process before they create a defective product or service. Statistics and Problem Solving Section 1.2 Statistics and Quality

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Statistics and Problem Solving 1.3 Descriptive versus Inferential Statistics Statistics and Problem Solving Section 1.3 Descriptive Versus Inferential Statistics Branches of Statistics: Descriptive statistics – the collection, organization, analysis, and presentation of data. The emphasis in descriptive statistics is analyzing observed measurements usually from a sample. To comprehend a large set of data, it must be summarized. That is the function of descriptive statistical techniques. Descriptive techniques are the most common statistical applications. Inferential statistics – uses descriptive statistics to estimate population parameters; an educated guess about the population based on sample data.

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Statistics and Problem Solving 1.3 Descriptive versus Inferential Statistics Statistics and Problem Solving Section 1.3 Descriptive Versus Inferential Statistics Example: In a survey of 100 students, 83.2% of students are happy with the food in the cafeteria. Identify the descriptive statistic(s). What inferences can be made? Descriptive statistic: 83.2% of the 100 students surveyed are happy with the food in the cafeteria. Possible inference: 83.2% of all students are happy with the food in the cafeteria. Solution: