MATH 2311 Introduction to Probability and Statistics

Size: px

Start display at page:

Download "MATH 2311 Introduction to Probability and Statistics"

Philomena Norman
6 years ago
Views:

1 MATH 2311 Introduction to Probability and Statistics Introduction Cathy Poliak, Ph.D. Department of Mathematics University of Houston Lecture 1 Lecture 1 1 / 31

2 Outline 1 Course Information and Introduction 2 Types of Data 3 Types of Variables 4 Describing Data By Graphs Lecture 1 2 / 31

3 Course Information Instructor: Dr. Cathy Poliak Webpage: Course webpage: Office: Fleming 11C Office Hours: Tuesdays and Thursdays 9:30 11:00 am and Wednesday 2:00 3:30 online using link meeting.jnlp?sid= &password=m A83AACD7CDB271EFB Lecture 1 3 / 31

4 Relevance of statistics Statistics is used to gather and analyze data for any discipline. (This is Statistics: Statistics is used to analyze surveys Lecture 1 4 / 31

5 What is Statistics? Statistics is used to make intelligent decisions in a world full of uncertainty. "A knowledge of statistics provides the necessary tool to differentiate between sound statistical conclusions and questionable conclusions." (Business Statistics Communicating with Numbers, Jaggia and Kelly, 2013, pg 4) Statistics is the science of collecting, organizing, and interpreting numerical facts which we call data. Lecture 1 5 / 31

6 A young fellow from had committed a grievous crime. Lecture 1 6 / 31

7 He had murdered his In Texas there is no excuse for murdering a horse. If the jury finds you guilty there is only one punishment. Hanging. Lecture 1 7 / 31

8 On the day of his hanging the warden talked to the prisoner and said, I am one of the few wardens that follows the law of 1889, and the law requires that I gather a random sample of 100 Texans. The warden dragged the prisoner to the auditorium and sure enough there were 100 Texans sitting there. The warden said, The law requires that I now give you an hour to speak to these people. The prisoner said, I have nothing to say. Lecture 1 8 / 31

9 Whereupon a professor in the audience stood up and said, I don t think the people of Texas know enough about statistics. If you are not going to use the hour, would you mind if I use it to educate these people about statistics? The prisoner said, No, go ahead. But the prisoner turned to the warden and said, BUT HANG ME FIRST! Lecture 1 9 / 31

10 What Will Be Taught In This Course? 1. Statistical methods can be used to summarize or describe a collection of data; this is called descriptive statistics. This is useful in research, when communicating the results of experiments. 2. Some tools in statistics requires the "chance" of an event happening. Thus we will also study a little bit of probability. 3. In addition, patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations, and are then used to draw inferences about the process or population being studied; this is called inferential statistics. Inference is a vital element of scientific advance, since it provides a prediction. See lecture schedule online. Lecture 1 10 / 31

11 Learning Objectives The student will be able to: Demonstrate the ability to understand basic theory of probability and statistics. Interpret statistical data. Understand statistical inference and interpretation. Apply statistical concepts to actual data. Lecture 1 11 / 31

12 Assessments Poppers 5% Online Quizzes 10% Homework 15% 3 Exams 45% Final Exam 25% The percentage grade on the final exam can be used to replace your lowest test score. Lecture 1 12 / 31

13 Poppers For each lecture starting on the third week of classes you will be asked a series of problems that will have to do with the lecture. This requires a buying a poppers package from the bookstore. Make sure that the package is for lecture 05 (section 14846). You are required to fill in your id number, popper number and blacken the correct circles. Make sure that your id number and popper number are correct before turning in the popper at the end of the lecture. If these are not filled out correctly or if the darken circles are too light you will not get credit for that day s lecture even if you attended. The total number of questions for the course will be counted, 85% of the total number of questions will be the 100%. For example, if there are 5 questions each class for 24 classes, which is 120 questions. Your grade will be calculated out of 120(.85) = 102 points. Lecture 1 13 / 31

14 Quizzes The quizzes are taken through the CourseWare website. Under "online assignments" The quizzes will close every Saturday at 11:59 pm starting on September 2nd. See your syllabus for the closed dates. One of the lowest quizzes will be dropped. You have up to 20 times to take each quiz. There is a 90 minute time limit for each quiz. Taking the quizzes until you get it right is essential to helping you do well on the exams and the homework. Lecture 1 14 / 31

15 Homework There are weekly assignments due every Wednesday starting on September 6th. The weekly homework assignments are worth 15 points. The homework will be submitted in the CASA CourseWare website. See instructions on the course web page for how to upload the homework. Two of the lowest homework scores will be dropped. Lecture 1 15 / 31

16 Exams Exam Chapters Covered Dates Exam 1 1, 2 and 3 September Exam 2 4, 5, and 6 October Exam 3 7 and 8 November 30 - December 2 Final Exam Comprehensive December 9-11 Lecture 1 16 / 31

17 Instructions of Exams All sections of Math 2311 take common exams. All exams will be given in CASA located on the second floor of Garrison, see the exam scheduler for details. You can access the scheduler for these exams by logging into Courseware. The scheduler will be available approximately 2 weeks prior to the start of the exam cycle. No make-up exams are given. The final exam score will replace your lowest test grade. Lecture 1 17 / 31

18 Textbook The textbook, online quizzes, and additional help materials will be made available by logging into CourseWare at The first portion of these materials are freely available for the first two weeks of class. All students must purchase a Course Access Code and enter it on CourseWare by Sunday September 3rd to continue accessing the course learning materials. A Course Access Code must be purchased for $55 from the University Bookstore. Lecture 1 18 / 31

19 Computer Software Knowledge of a statistical package is an indispensable part of the modern statistics. The class presentations, some homework assignments, and the exams are computer based. The statistical package R-studio is used in this class for exploring statistical concepts and demonstrating statistical analysis of actual data useful for business decisions. No previous knowledge of this software is assumed. This software is a free package that you can download on to your personal computer. This will be available to you for your exams in CASA. You first need to download R: Then you can download Rstudio: Lecture 1 19 / 31

20 Other Information This is a challenging course. Each student is responsible for his/her learning. If a section of the textbook and/or homework problem is puzzling you, it is your responsibility to make an appointment to see the instructor or a tutor as soon as possible. You are encouraged to ask questions during lectures and office hours. The following are the recourses available to you for help in this course. Instructor: You are always welcome in the instructor s office for help. If the office hours are not convenient for you just the instructor or post your question on the discussion board. CASA Tutoring ( Garrison Gym 222, see instructor s webpage for times of tutors for LAUNCH ( N109 Cougar Village Lecture 1 20 / 31

21 A Data Set: Course Grades From Last Year Student Score Grade Tests Quiz HW Opt-out Session A yes Sp B yes Sp F no Sp A yes Sp D no Sp A yes Sp A no Sp B yes Sp A yes Sp F no Sp A yes Sp F no Sp F no Sp F no Sp F no Sp A yes Sp B yes Sp B yes Sp D no Fal B yes Fal D no Fal C no Fal F no Fal A no Fal F no Fal B no Fal B no Fal C no Sum B yes Sum A no Sum16 Lecture 1 21 / 31

22 Types of data Population Datai s everything or everyone we want information about. It is a set of data that consists of all possible values pertaining to a certain set of observations or an investigation. Sample Data is a subset of the population that we have information from. It is just a small section of the population taken for the purpose of investigation. Lecture 1 22 / 31

23 Examples of Types of Data Identify the population and the sample for each of the following: University of Houston is interested in how many students buy used books as opposed to new ones. They randomly choose 100 students at the student center to interview Population - Sample - An elementary school is creating a new lunch menu. They send questionnaires to students with last names that begin with the letters M through R. Population - Sample - Lecture 1 23 / 31

24 Two Types of Variables Go back to the example of grades. We have several variables, score, grade, tests, quiz, hw, opt-out, & session. The variables grade, opt-out, & session are categorical variables. Categorical variables place a case into one of several groups or categories. The variables scores, tests, quiz & hw is a quantitative variable. Quantitative Variables take numerical values for which arithmetic operations such as adding and averaging make sense. Lecture 1 24 / 31

25 Two Types of Quantitative Variables Quantitative variables can be classified as either discrete or continuous. Discrete quantitative variables - a countable set of values. Continuous quantitative variables - data that can take on any values within some interval. Lecture 1 25 / 31

26 Examples of Variables Classify the following variables as categorical or quantitative. If quantitative, state whether the variable is discrete or continuous. Political preference. Number of siblings. Lecture 1 26 / 31

27 Examples of Variables Part 2 Classify the following variables as categorical or quantitative. If quantitative, state whether the variable is discrete or continuous. Blood type. Height of men on a professional basketball team. Time it takes to be on hold when calling the IRS at tax time. Lecture 1 27 / 31

28 Describing Data By Graphs Graphs are an easy and quick way to describe the data. Types of graphs that we use depends on the type of data that we have. Graphs for categorical variables. Bar graphs: Each individual bar represents a category and the height of each of the bars are either represented by the count or percent. Pie charts: Helps us see what part of the whole each group forms. Graphs for quantiative variables. Dotplot Stemplot Histogram Boxplot Lecture 1 28 / 31

29 Bar Graph of Letter Grades A B C D F Lecture 1 29 / 31

30 Pie Chart of Letter Grades A B C D F Lecture 1 30 / 31

31 R code First create a table: counts = table(grades$grade) For bar graph: barplot(counts) For pie chart: pie(counts) Lecture 1 31 / 31

Class Meeting Time and Place: Section 3: MTWF10:00-10:50 TILT 221

Class Meeting Time and Place: Section 3: MTWF10:00-10:50 TILT 221 Math 155. Calculus for Biological Scientists Fall 2017 Website https://csumath155.wordpress.com Please review the course website for details on the schedule, extra resources, alternate exam request forms,