Introduction to Statistics

1. Introduction to Statistics 1 As you view these slides be sure to have paper, pencil, a calculator and your text handy. Click to advance to the slide show. Elementary Statistics Larson Farber

2. Section 1.1 An Overview of Statistics

3. Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions. What is Statistics?

4. Important Terms x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x • Population The collection ofallresponses, measurements, or counts that are of interest. • Sample A portion or subset of the population.

5. Identifying Data Sets In a recent survey, 3002 adults in the United States were asked if they read news on the Internet at least once a week. Six hundred of the adults said yes. Identify the population and the sample. Population: Responses of all adults in the U.S. Sample: Responses of the 3002 adults in the U.S.

6. Important Terms • Parameter: A number that describes a population characteristic. Average gross income of all people in the United States in 2002. • Statistic: A number that describes asample characteristic. 2002 gross income of people from a sample of three states.

7. Parameter or Statistic? Decide whether the numerical value describes a population parameter or a sample statistic. Explain your reasoning. • A recent survey of a sample of MBAs reported that the • average starting salary for an MBA is less than $65,000. Sample Statistic: b/c $65,000 is based on a subset of the population. • Starting salaries for the 667 MBA graduates from the • University of Chicago Graduate School of Business increased • 8.5% from the previous year. Population Parameter: b/c 8.5% is based on all 667 graduates. • In a random check of a sample of retail stores, the Food and • Drug Administration found that 34% of the stores were not • storing fish at the proper temperature. Sample Statistic: b/c 34% is based on a subset of the population.

8. Two Branches of Statistics Descriptive StatisticsInvolves organizing, summarizing, and displaying data. Inferential StatisticsInvolves using sampledata to draw conclusions about a population.

9. Section 1.2 Data Classification

10. Types of Data Qualitative Data: Consist of attributes, labels, or no numerical entries. Quantitative Data: Consist of numerical measurements of counts.

11. Classifying Data by Type The base prices of several vehicles are shown in the table. Which data are qualitative data and which are quantitative data? Explain your reasoning? The names of the vehicle models: Qualitative Data The base price of the vehicles: Quantitative Data

12. Levels of Measurement 1. Nominal 2. Ordinal 3. Interval 4. Ratio A data set can be classified according to the highest level of measurement that applies. The four levels of measurement, listed from lowest to highest are:

13. Levels of Measurement Categories, names, labels, or qualities. Cannot perform mathematical operations on this data. 1st place 1. Nominal: Ex:type of car you drive, your major 2. Ordinal: Data can be arranged in order. You can say one data entry is greater than another. Ex:TV ratings, condition of patient in hospital.

14. Levels of Measurement Data can be ordered and differences between 2 entries can be calculated. There is no inherent zero (a zero that means “none”.) 3. Interval: Ex: Temperature, year of birth There is an inherent zero. Data can be ordered, differences can be found, and a ratio can be formed so you can say one data value is a multiple of another. 4. Ratio: Ex.money

15. Section 1.3 Experimental Design

16. Random Sample: Each member of the population has an equal chance of being selected. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Simple Random Sample:All samples of the same size are equally likely. • Assign a number to each member of the population. • Random numbers can be generated by a random number table, software program or a calculator. • Data from members of the population that correspond to these numbers become members of the sample.

17. Stratified Random Samples Divide the population into groups (strata) and select a random sample from each group. Strata could be age groups, genders or levels of education, for example. Sample

18. Cluster Samples Divide the population into individual units or groups and randomly select one or more units. The sample consists of all members from selected unit(s). Cluster Sample:

19. Systematic Samples Choose a starting value at random. Then choose sample members at regular intervals. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x We say we choose every kth member. In this example, k = 5. Every 5th member of the population is selected.

20. Other Samples Convenience Sample:Choose readily available members of the population for your sample.

21. Data Collection • Experiment: Apply a treatment to a part of the group. • Simulation: Use a mathematical model (often with a computer) to reproduce condition. • Census: A count or measure of the entire population • Sampling: A count or measure of part of the population.