Statistics and Problem Solving

1. Statistics and Problem Solving Chapter 1

2. HAWKES LEARNING SYSTEMS math courseware specialists Statistics and Problem Solving Sections 1.1-1.3 Getting Started Objectives: • Learn the basic vocabulary of statistics. • Distinguish between populations and samples. • Distinguish between parameters and statistics.

3. Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? 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.

4. Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? What Methods do Statisticians Use to Make Predictions? • Populations • Frames • Population Parameters • Samples • Sample Statistics

5. 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? Statistics and Problem Solving 1.1 Who will be the 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.

6. 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. Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Statistics and Problem Solving 1.1 Who will be the next president? Examples of Populations: • Can you think of any examples of populations?

7. Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Statistics and Problem Solving 1.1 Who will be the 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.

8. 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. Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Statistics and Problem Solving 1.1 Who will be the next president? Examples of Frames: • Can you think of any examples of frames?

9. Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Statistics and Problem Solving 1.2 Statistics and Quality 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.

10. Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? 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 18-25 who favor a candidate. • The average income of the voters who favor a candidate.

11. Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Statistics and Problem Solving 1.2 Statistics and Quality 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. • Can you think of any examples of population parameters?

12. Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Statistics and Problem Solving 1.2 Statistics and Quality 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.

13. Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Statistics and Problem Solving 1.2 Statistics and Quality Definition: A statistic is a fact or characteristic about a sample. Example: 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.

14. Statistics and Problem Solving Section 1.1 Who Will Be Our Next President? Statistics and Problem Solving 1.2 Statistics and Quality Question Defines Population/Variables Estimate Parameter Calculate Statistic Collect Data

15. Statistics and Problem Solving Section 1.2 Statistics and Quality 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.

16. Statistics and Problem Solving Section 1.3 Descriptive Versus Inferential Statistics Statistics and Problem Solving 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.

17. Statistics and Problem Solving Section 1.3 Descriptive Versus Inferential Statistics Statistics and Problem Solving 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: