QMM 280

1. QMM 280 Introduction to Statistics Dr. Barry A. Wray Associate Professor Department of IS and OM

2. Introduction • What is a definition for statistics? • The field of Statistics is concerned with the collection, presentation, and analysis of data in order to assist a manager in the decisions making process. • What is the “story” of the data?

3. Two Main Branches of Statistics Descriptive Inferential Infer or make conclusions from an analysis of the data • Describe the data • Central Tendency • Dispersion • Distribution

4. Sources of Data • Survey Data • Historical Records • Published Data • Manufacturing Data • Sales Data

5. TYPES OF DATA • QUALITATIVE • Data which is non numerical • QUANTITATIVE (Continuous) • Data which is numerical in nature

6. QUALITATIVE • NOMINAL • Data classified into categories with no order implied • What color are your eyes? • What is your Occupation? • Accountant • Economist • Manager • Teacher • Unemployed (Student) • ORDINAL • Categorical data with ordering implied • How was the movie last night? • Excellent • Very Good • Good • Fair • Poor

7. QUANTITATIVE (Continuous) • Discrete • Usually integer values • Number of people • Number of defective items • Continuous • Fractional values • Weight • Age • Height • Time

8. Types of Data • Time Series Data is data collected through time. • Stock prices are an example of time series data. Tomorrow’s starting price for a stock depends on the ending price of that stock today. Stock prices “move” over time so it is important to factor in this effect. • Cross Sectional Data does not have a “time” component • Data collected on a variable at a single point in time. For example you might be interested in doing a study of comparative housing prices for the 8 major cities in June 2000.

9. Examining the Data • First step in any analysis is to examine the data • Arrays • Listing the data in ascending or descending order. • Useful in identifying common or outlying values • Tables • Summarizing the data into categories • Useful for visualizing important characteristics of the data • Frequency Distributions • Graphical Representations • Pie and Bar Charts • Histograms

10. Descriptive Measures • Central Tendency • Mean • Median • Mode • Dispersion • Range • Mean Absolute Deviation • Standard Deviation

11. Statistical Terminology • Population – the collection of ALL entities possessing some characteristic we are interested in. • Sample – some subset of a Population • Population Parameter – a summary measure of some characteristic we are interested in for all entities in a population. • sample statistic – a summary measure computed from a sample and used to estimate a Parameter from the Population where the sample was derived from.

12. Selecting a sample • Why sample? • Cost and time advantages • Population size - Census too cumbersome • Destructive sampling

13. simple random sampling (srs) • Definition • Each member of the population has an equally likely chance of being selected. • sampling with replacement • Basis of most statistical inference

14. Errors in Collecting Data • sampling error • Error caused because no sample is exactly representative of population • Chance differences that occur when a sample is selected • Non sampling error • Error caused by human.

15. Population Parameters are computed from a census of the entire Population and are used to describe some characteristic about the Population you are interested in (X). Population µx Parameters sx

16. Population Parameters are computed from a census of the entire Population and are used to describe some characteristic about the Population you are interested in (X). Population µx Parameters sx A sample is a subset of a larger Population sample sx sample statistics are computed from sample data and used to estimate Population Parameters statistics