Statistics Lecture Notes Dr. Halil İbrahim CEBECİ Chapter 01 What is statistics?

Simple Explanation: Statistics is a way to get information from data Statistics is the study of the collection, organization, analysis, interpretation, and presentation of data What do statisticians do? Statisticians contribute to scientific enquiry by applying their knowledge to the design of surveys and experiments; the collection, processing, and analysis of data; and the interpretation of the results What is statistics? Statistics Lecture Notes – Chapter 01

What is statistics? Statistics Lecture Notes – Chapter 01 Data Statistics Information Data: Facts, especially numerical facts, collected together for reference or information. 55,68,39,43 Information: Knowledge communicated concerning some particular fact. Class average, Most frequent mark, Marks distribution, etc. Statistics is a tool for creating new understanding from a set of numbers.

Why? Because numeric and non-numeric data are everywhere In marketing, accounting, finance, economics, politics, sciences, and elsewhere, there are statistics We need to be able to understand statistics when we encounter them We need to not be tricked by misleading statistics We need to use statistics to help us make decisions under future uncertainty What is statistics? Statistics Lecture Notes – Chapter 01

Where? Research analysts for Merrill Lynch evaluate many facets of a particular stock before making a “buy” or “sell” recommendation. The marketing department at Colgate-Palmolive Co., a manufacturer of soap products, has the responsibility of making recommendations regarding the potential profitability of a newly developed group of face soaps having fruit smells. The United States government is concerned with the present condition of our economy and with predicting future economic trends. Managers must make decisions about the quality of their product or service. What is statistics? Statistics Lecture Notes – Chapter 01

Descriptive statistics Collecting (eg.Survey, Experiment and Observation), presenting(eg. Bar Charts and Graphs), and describing data (eg. Mean) Inferential statistics Drawing conclusions and/or making decisions concerning a population based only on sample data Key statistical concepts Statistics Lecture Notes – Chapter 01

Population a population is the group of all items of interest to a statistics practitioner. frequently very large; sometimes infinite. E.g. All 5 million Florida voters, per Example 12.5 Sample A sample is a set of data drawn from the population. Potentially very large, but less than the population. E.g. a sample of 765 voters exit polled on election day. Key statistical concepts Statistics Lecture Notes – Chapter 01

Key statistical concepts Statistics Lecture Notes – Chapter 01 Parameter ( A descriptive measure of a population) Sample Statistic (A descriptive measure of a sample) Subset Population

Descriptive Statistics Statistics Lecture Notes – Chapter 01 According to Consumer Reports, General Electric washing machine owners reported 9 problems per 100 machines during The statistic 9 describes the number of problems out of every 100 machines.

are methods of organizing, summarizing, and presenting data in a convenient and informative way. These methods include:  Graphical Techniques and,  Numerical Techniques The actual method used depends on what information we would like to extract. Are we interested in…  measure(s) of central location? and/or  measure(s) of variability (dispersion)? Descriptive Statistics Statistics Lecture Notes – Chapter 01

Descriptive Statistics describe the data set that’s being analyzed, but doesn’t allow us to draw any conclusions or make any interferences about the data. Hence we need another branch of statistics: inferential statistics. Inferential statistics is also a set of methods, but it is used to draw conclusions or inferences about characteristics of populations based on data from a sample. Statistical Inference Statistics Lecture Notes – Chapter 01

Statistical inference is the process of making an estimate, prediction, or decision about a population based on a sample. Statistical Inference Statistics Lecture Notes – Chapter 01 What can we infer about a Population’s Parameters based on a Sample’s Statistics?

Rationale:  Large populations make investigating each member impractical and expensive.  Easier and cheaper to take a sample and make estimates about the population from the sample. However:  Such conclusions and estimates are not always going to be correct. For this reason, we build into the statistical inference “measures of reliability”, namely confidence level and significance level. Statistical Inference Statistics Lecture Notes – Chapter 01

Ex1.1 - According to USAToday (15 October 1987), the average size of an American household had fallen from 3.14 persons in 1970 to 2.66 persons in a.The 1987 figure of 2.66 is claimed to be the value of a population parameter. What are the population and the parameter? b.What procedure must be taken to be 100% certain that the value of the population parameter is exactly 2.66? c.What procedure was likely used to arrive at the 1987 figure of 2.66? Use the terms sample, sample statistic, and inference in your answer. Examples Statistics Lecture Notes – Chapter 01

A1.1a - One can imagine determining the number of persons living in each and every household in the United States. The set of all these (millions of) numbers is the population of interest. The average of this population of numbers is the parameter of interest, which is claimed to be A1.1b - You would have to collect all the numbers in the population (called taking a census) and then compute the average of all the numbers. Examples Statistics Lecture Notes – Chapter 01

A1.1c - It is likely that only a relatively small subset of all American households was selected and the number of persons living in each of these households obtained. The set of numbers obtained for the selected group of households is a sample drawn from the population. The average of the sample values, called the sample statistic, was then computed to be The statement that 2.66 is the average size of all American households is an inference about the population parameter; it may or may not be correct. Examples Statistics Lecture Notes – Chapter 01

Q1.1 - Thousands of customers have accounts at a large department store. An accountant claims that the average unpaid balance for these accounts is $75, a figure obtained by computing the average of the unpaid balances for 50 of the accounts. a.Identify the population and its parameter. b.What is the sample? c.Is the figure of $75 a parameter or a statistic? Exercises Statistics Lecture Notes – Chapter 01

Q1.2 - A psychologist has interviewed 250 school children throughout New York State and found that 80% of them spend at least 25 hours a week watching television. a.Identify the population parameter and the sample statistic of interest here b.Comment on the following inference, which is based on the results of the psychologist’s interviews: 80 percent of American school children spend at least 25 hours a week watching television. Exercises Statistics Lecture Notes – Chapter 01

 Keller, Gerald; Statistics for Management and Economics, 9e, 2012  Groebner, D.F.; Shannon, P.W., Fry, P.C, Smith, K.D; Business Statistics: A decision Making Approach, 7e, 2007  McClave, J.T, Benson, P.G, Sincich, T.; Statistics for Business and Economics, 11e, 2011 References Statistics Lecture Notes – Chapter 01