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  1. 1. Math 1127 Introductory Statistics Dr. Carlos Almada Office: 212 University Hall Office Hours: Wed 7-11 am
  2. 2. Math 1127: Class Format My share  Lectures, Blackboard, Powerpoint, Slides  Problem Solving  Discussion  Office Hours Your share  Be prepared!  Arrive on time  Stay until end of session  Do the homework  Provide feedback
  3. 3. Stats … Before
  4. 4. Stats … After
  5. 5. Class Web Page: Go to http://facstaff.columbusstate.edu/almada_carlos/ Click on Math 1127: Introductory Statistics
  6. 6. Overview Of Statistics
  7. 7.  Recent news programs have found that dairies companies have been under filling milk containers sent to public school lunch programs. This under filling of containers costs school districts, that is, taxpayers, mega-bucks. How could you discover if containers in your school district were being under filled? Typical Problem
  8. 8. Allen Benning Hills Blanchard Brewer Britt David Elementary Computer Magnet Academy Clubview Cusseta Road Davis Dawson Dimon Elementary Double Churches Downtown Elementary Magnet Academy Eastway Edgewood Forrest Road Fox Public Elementary Schools Gentian Georgetown Hannan Elementary Johnson Key Martin Luther King, Jr. Mathews Midland Academy Muscogee North Columbus Elementary Reese Road Rigdon Road River Road South Columbus St. Marys Video and Communication Technology Waddell Wesley Heights Wynnton
  9. 9. Middle Arnold Baker Blackmon Road Double Churches East Columbus Magnet Academy Eddy Fort Marshall Midland Richards Rothschild High Anne Elizabeth Sheperd Home Carver Columbus Early College Academy of Columbus Hardaway Jordan Vocational Kendrick Northside Shaw Spencer Public Middle/High Schools
  10. 10. Number of Students in 2008: 33,502 Economically Disadvantaged: 61.00% Students with Disabilities: 12.00% English Language Learners: 2.00% Did this District make Adequate Yearly Progress in 2008? No District Facts for 2008
  11. 11. Chapter 1 Introduction to Statistics  Overview  Variables and Types of Data
  12. 12. Introduction to Statistics  Definition: Statistics is the science of C Collecting … O Organizing … D Displaying … I Interpreting … A Analyzing … Data in order to make decisions.
  13. 13.  “Data” is the plural of “Datum” (Latin for “given”).  Consists of information coming from counts, observations, measurements, or responses on a set of objects.  The objects can be anything…, e.g., people, animals Introduction to Statistics
  14. 14.  Definition of Population and Sample  Population: the complete collection of all individuals or objects (scores, people, measurements, and so on) to be studied.  Sample: a subcollection of members selected from a population and from which the desired information is collected. Introduction to Statistics
  15. 15.  Definition of Population and Sample Introduction to Statistics
  16. 16. Therefore, There Is  Population Data or Census Consists of data collected from every member of a population  Sample Data Consists of data collected from the members of a sample of a population
  17. 17. Population and Sample Example: In a recent survey, 250 college students at Union College were asked if they smoked cigarettes regularly. 35 of the students said yes. Identify the population and the sample. Responses of all students at Union College (population) Responses of students in survey (sample)
  18. 18. Parameters and Statistics Parameter Population Statistic Sample  A parameter is a numerical description of a population characteristic.  A statistic is a numerical description of a sample characteristic.
  19. 19. Example: Decide whether the numerical value describes a population parameter or a sample statistic.  A recent survey of a sample of 450 college students reported that the average weekly income for students is $325. Because the average of $325 is based on a sample, this is a sample statistic.  The average weekly income for all students is $405. Because the average of $405 is based on a population, this is a population parameter. Parameters and Statistics
  20. 20. Branches of Statistics  The study of statistics has two major branches: descriptive statistics and inferential statistics. Statistics Descriptive statistics Inferential statistics Involves organizing, summarizing, and displaying data. Involves using a sample to draw conclusions about a population.
  21. 21. Descriptive and Inferential Statistics Example: In a recent study, volunteers who had less than 6 hours of sleep were four times more likely to answer incorrectly on a science test than were participants who had at least 8 hours of sleep. Decide which part is the descriptive statistic and what conclusion might be drawn using inferential statistics. The statement “four times more likely to answer incorrectly” is a descriptive statistic. An inference drawn from the sample is that all individuals sleeping less than 6 hours are more likely to answer science questions incorrectly than individuals who sleep at least 8 hours.
  22. 22. Descriptive and Inferential Statistics
  23. 23. Step 1: Identify a Research Objective • Researcher must determine question he/she wants answered. • Identify the group to be studied. This group is called the population. • An individual is a person or object that is a member of the population being studied The Process of Statistics
  24. 24. Step 2: Collect the information needed to answer the questions. • In conducting research, we typically look at a subset of the population, called a sample. Step 3: Organize and summarize the information. • Descriptive statistics consists of organizing and summarizing the information collected. Consists of charts, tables, and numerical summaries. The Process of Statistics
  25. 25. Step 4: Draw conclusions from the information. • The information collected from the sample is generalized to the population. • Inferential statistics uses methods that generalize results obtained from a sample to the population and measure their reliability. The Process of Statistics
  26. 26. Data Collection Simple Random Sampling
  27. 27. We say that a sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring. The sample is then called a simple random sample. Simple Random Sampling (SRS) In chapter 6 we will be interested in all possible samples of a fixed size that can be selected from a given population
  28. 28. Suppose a study group of consists of 5 students: Bob, Patricia, Mike, Jan, and Maria. Two of the students must go to the board to demonstrate a homework problem. List all possible samples of size 2 (without replacement). • Bob, Patricia • Bob, Mike • Bob, Jan • Bob, Maria • Patricia, Mike • Patricia, Jan • Patricia, Maria • Mike, Jan • Mike, Maria • Jan, Maria Simple Random Sampling (SRS)
  29. 29. Steps for Obtaining a SRS  Obtain a frame that lists all the individuals in the population of interest.  Number the individuals in the frame 1 - N.  Use a graphing calculator, or statistical software to randomly generate n numbers where n is the desired sample size.
  30. 30. Variables and Data
  31. 31. Variables  Variables are the characteristics of the individuals within the population.  Mathematically speaking, a variable is a function that assigns to each member of a population an output that can be numerically or non-numerically valued.  According to this output we have…..
  32. 32. A Qualitative or Categorical variable allows for the classification of individuals based on some attribute or characteristic. It is a non-numerically valued variable. A Quantitative variable provides numerical measures of individuals. Arithmetic operations such as addition and subtraction can be performed on the values of the quantitative variable and provide meaningful results. Two Types of Variables
  33. 33. Determine whether the following variables are qualitative or quantitative. a) Type of wood used to build a kitchen table. b) Number of yards Tiger Woods hits his drives. c) Number of times your Internet service goes down in the next 30 days. Examples of Variables
  34. 34. More Examples of Variables  Age, Height, Weight  Grade in Math 1127 (A=4, B=3, etc.)  Temperature (K, F, C)  Male (0), Female (1), Androgynous (2)  Test score (e.g., SAT)
  35. 35. A discrete variable is a quantitative variable that either has a finite number of possible values or a countable number of possible values. A continuous variable is a quantitative variable that has infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps. A continuous variable can be measured to any desired level of accuracy. Types of Quantitative Variables
  36. 36. Determine whether the following quantitative variables are continuous or discrete. a) Number of yards Tiger Woods hits his drives. b) Number of times your Internet service goes down in the next 30 days. Types of Quantitative Variables
  37. 37. Variables
  38. 38. Data  The list of observations a variable assumes is called data.  While gender is a variable, the observations, male or female, are data.  According to the type of data the variables represents, we can have ……
  39. 39. Qualitative data are observations corresponding to a qualitative variable. Quantitative data are observations corresponding to a quantitative variable. Discrete data are observations corresponding to a discrete variable. Continuous data are observations corresponding to a continuous variable. Data
  40. 40.  Each row records data on one individual.  Each column contains the values of one variable for all the individuals. Here is part of the data set (a spreadsheet) in which Cyber Stat Corporation records information about its employees: Example of Variables and Data