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Induction Course Outline (PGDM A/B/IB/RM/IMC/FS) Subject: Business Statistics Batch of 2012-14 Session Topics I – What is Statistics? Definition of Statistics Descriptive Statistics vs Inferential Statistics Population and Samples Test your knowledge II – Types of Data Variable, values and data Nominal, ordinal, interval and ratio data Statistical measures used for different types of data III – Graphical method Frequency, Relative Frequency, Cumulative frequency, Class Intervals. Bar charts, Pie charts and Histograms Shape of histogram – symmetry vs skewness Home assignment -Time Series Data and Relation between two variables IV – Numerical descriptive Measures of Central Tendency and Dispersion techniques Reference Books Business Statistics in Practice - Bowerman Statistics for Management – Gerald Kellar Statistics for Business and Economics – Andersen and Sweeney Statistics for Management – Levin and Rubin Business Statistics – Levine and Krehbiel Applied statistics in business and economics- Donae & Seward Session 1: What is Statistics Statistics Anxiety!! A student enrolled in the first year business program is attending the first class of the required statistics course. The student is somewhat apprehensive because he believes the myth that the course is difficult. To alleviate his anxiety the student asks the professor about last year’s marks. The professor obliges and provides a list of the final marks, which is composed of term work plus the final exam. What information can you obtain from the list? Descriptive statistics deals with methods of organizing, summarizing, and presenting data in a convenient and informative way. Inferential statistics is a body of methods used to draw conclusions or inferences about characteristics of populations based on sample data. Population — a population is the group of all items of interest to a statistics practitioner. — frequently very large; sometimes infinite. Sample — A sample is a set of data drawn from the population. — Potentially very large, but less than the population. Statistical inference is the process of making an estimate, prediction, or decision about a population based on a sample. Statistical analysis plays an important role in virtually all aspects of business and economics. Throughout this course, we will see applications of statistics in accounting, economics, finance, human resources management, marketing, and operations management. Test your Knowledge Please select the right option 1. You take a random sample of 100 students at your university and find that their average GPA is 3.1. If you use this information to help you estimate the average GPA for all students at your university, then you are doing what branch of statistics? a. Descriptive statistics b. Inferential statistics c. Sample statistics d. Population statistics 2. A company has developed a new computer sound card whose average lifetime is unknown. In order to estimate this average, 200 sound cards are randomly selected from a large production line and tested; their average lifetime is found to be 5 years. The 200 sound cards represent a: a. parameter. b. statistic. c. sample. d. population. 3. A company has developed a new computer sound card whose average lifetime is unknown. In order to estimate this average, 200 sound cards are randomly selected from a large production line and tested; their average lifetime is found to be 5 years. The 5 years represents a: a. parameter. b. statistic. c. sample. d. population. 4. A descriptive measure that is computed from a sample is called a: a. parameter. b. statistic. c. population. d. sample. 5. A summary measure that is computed from a population is called a: a. sample. b. statistic. c. population. d. parameter. 6. Which of the following is a measure of the reliability of a statistical inference? a. A population parameter. b. A significance level. c. A descriptive statistic. d. A sample statistic. 7. A politician who is running for the office of governor of a state with 4 million registered voters commissions a survey. In the survey, 54% of the 5,000 registered voters interviewed say they plan to vote for her. The population of interest is: a. the 4 million registered voters in the state. b. the 5,000 registered voters interviewed. c. the 54% who plan to vote for her. d. all the residents of the state. 8. A company has developed a new battery and wants to estimate its average lifetime. A random sample of 500 batteries is tested and the average lifetime of this sample is found to be 225 hours. The 225 hours is the value of a: a. parameter. b. statistic. c. sample. d. population. 10. Which of the following represents a population, as opposed to a sample? a. 1,000 respondents to a magazine survey which has 500,000 subscribers. b. The first 10 students in your class completing a final exam. c. Every fifth student to arrive at the book store on your campus. d. All registered voters in the State of Michigan. 11. A researcher at Michigan State University (MSU) wants to estimate the average number of credits earned by students last semester at MSU. She randomly selects 500 students from last semester and finds that they averaged 14.85 credits per student. The population of interest to the researcher is: a. all MSU students. b. all college students. c. all MSU students enrolled last semester. d. the 500 MSU students selected at random. 12. A study is under way to determine the average height of all 32,000 adult pine trees in a certain national forest. The heights of 500 randomly selected adult pine trees are measured and analyzed. The sample in this study is: a. the average height of the 500 randomly selected adult pine trees. b. the average height of all the adult pine trees in this forest. c. all the adult pine trees in this forest. d. the 500 adult pine trees selected at random from this forest. 13. A study is under way to determine the average height of all 32,000 adult pine trees in a certain national forest. The heights of 500 randomly selected adult pine trees are measured and analyzed. The parameter in the study is: a. the average height of the 500 randomly selected adult pine trees. b. the average height of all the adult pine trees in this forest. c. all the adult pine trees in this forest. d. the 500 adult pine trees selected at random from this forest. State Whether True or False with justification 1. A university employs 2,500 faculty and staff. To ascertain their employees' opinions of a proposed health insurance plan, 250 employees are surveyed at random. The proportion of the 250 employees who favor the health insurance plan represents a parameter in this scenario. 2. In a sample of 400 students selected from a large college of business, 30% are found to be marketing majors. The 30% is a statistic. 3. Twenty-five percent of a sample of 200 professional tennis players indicated that their parents did not play tennis. Based on this sample, we estimate that approximately 25% of the parents of all professional tennis players did not play tennis, plus or minus 5%. This is an example of using inferential statistics. 4. A population is the group of all items of interest to a statistics practitioner. 5. A descriptive measure of a population is called a parameter. 6. A descriptive measure of a sample is called a parameter. 7. You take a random sample to estimate a population mean and your results have a confidence level of 90%. That means the process you used will give you correct results 90% of the time. Fill in the Blanks 1. The Human Resources Director of a large insurance company wishes to develop a new employee health benefits package. She selects 400 employees at random and asks them about their preferences regarding their current health benefits package. The 400 employees selected is a(n) ____________________. 2. Each of the following is a form of doing ____________________ statistics: 1) presenting your data using a graph; 2) calculating the mean of your sample; and 3) organizing your data into a table. 3. The Commissioner of Health in California State wanted to study malpractice litigation in Los Angeles last year. She randomly selected 32,000 medical records from the population of 3.5 million patients in Los Angeles last year. The proportion of malpractice claims filed from the 32,000 patients is an example of a(n) ____________________. Assignments: 1. At Grand Rapids Community College, administrators want to determine the average commuting distance for their students who commute to school. They randomly select 150 students who commute and ask them the distance of their commute to campus. From this group a mean of 18.2 miles is computed. a. Describe/find the parameter. b. Describe/find the statistic. c. Describe the population. d. Describe the sample. 2. Briefly describe the difference between a parameter and a statistic, and give an example of each. 3. Briefly describe the difference between a population and a sample and give an example of each. 4. A manufacturer of children's toys wants to know what percentage of all of their toys are defective. When 500 of their toys are selected at random and examined, 0.5% are found to be defective. a. Describe the population of interest. b. Describe the sample. c. Describe/find the parameter. d. Describe/find the statistic. e. Is the 0.5% a parameter or a statistic in this scenario? Why? 7. A lawyer who is running for the vacant City Mayor seat with 25,000 registered voters wants to determine what percentage would vote for her. Her pollsters interview 500 registered voters from the city at random; 55% say they plan to vote for her. a. What is the population of interest? b. What is the sample? c. Is the 55% a parameter or a statistic in this scenario? Why? 8. Define each of the following statistical terms: a. Descriptive statistics b. Statistical inference c. Confidence level d. Significance level e. Population f. Sample 9. Identify each of the following as a use of descriptive statistics or inferential statistics. a. Finding the weights of a sample of 75 manufacturer parts. b. Calculating the average weight of 100 boxes shipped by UPS. c. Estimating the percentage of the U.S. population that will vote for your favorite candidate in the next presidential election. d. Selecting a random sample of 100 babies born last year and using this information to estimate the birth weight of all babies born last year. e. Randomly selecting 100 cans of a brand of corn and using their average weight to decide whether the 16 oz. label on the cans is truthful or not. Session 2: Types of Data and Tabular Descriptive Techniques Descriptive statistics involves arranging, summarizing, and presenting a set of data in such a way that useful information is produced. Its methods make use of graphical techniques and numerical descriptive measures (such as averages) to summarize and present the data. A variable is some characteristic of a population or sample. E.g. student grades. The values of the variable are the range of possible values for a variable. E.g. student marks (0..100) Data are the observed values of a variable. E.g. student marks: {67, 74, 71, 83, 93, 55, 48} There are 4 types of Data: Nominal, Ordinal, Interval and Ratio Hierarchy of Data Ratio Values are real numbers. True origin exists All calculations are valid. Data may be treated as ordinal or nominal. Interval Values are real numbers. True origin does not exist, however numbers are equidistant All calculations are valid. Data may be treated as ordinal or nominal. Ordinal Values must represent the ranked order of the data. Calculations based on an ordering process are valid. Data may be treated as nominal but not as interval or ratio. Nominal Values are the arbitrary numbers that represent categories. Only calculations based on the frequencies of occurrence are valid. Data may not be treated as ordinal or interval. Multiple Choice Questions 1. The classification of student major (accounting, economics, management, marketing, other) is an example of a(n) a. nominal random variable. b. interval random variable. c. continuous random variable. d. parameter. 2. The classification of student class designation (freshman, sophomore, junior, senior) is an example of a(n) a. nominal random variable. b. interval random variable. c. ordinal random variable. d. a parameter. 3. A researcher wishes to estimate the textbook costs of first-year students at Ferris State University. To do so, he recorded the textbook cost of 200 first-year students and found that their average textbook cost was $275 per semester. The variable of interest to the researcher is a. textbook cost. b. class rank. c. number of students. d. name of university. 4. All calculations are permitted on what type of data? a. Interval data b. Nominal data c. Ordinal data d. All of these choices are true. 5. Values must represent ordered rankings for what type of data? a. Interval data b. Nominal data c. Ordinal data d. None of these choices. 6. For what type of data are frequencies the only calculations that can be done? a. Interval data b. Nominal data c. Ordinal data d. None of these choices. 7. For which type of data are the values arbitrary numbers? a. Interval data b. Nominal data c. Ordinal data d. None of these choices. TRUE/FALSE 8. Your gender is a nominal variable. 9. Your final grade in a course (A, B, C, D, E) is a nominal variable. 10. Your age is an interval variable. 11. Your age group (1-10; 11-20; 21-30; 31-40; etc.) is an interval variable. 12. Whether or not you are over the age of 21 is a nominal variable. 13. The values of quantitative data are categories. 14. Interval data, such as heights, weights, and incomes, are also referred to as quantitative or numerical data. 15. Nominal data are also called qualitative or categorical data. 16. A variable is some characteristic of a population or sample. 17. With nominal data, there is one and only one way the possible values can be ordered. 18. You cannot calculate and interpret differences between numbers assigned to nominal data. 19. All calculations are permitted on interval data. 20. Interval data may be treated as ordinal or nominal. COMPLETION 21. The Dean of Students conducted a survey of students on campus. A student's SAT score in mathematics is an example of a(n) ____________________ variable. 22. The Dean of Students conducted a survey on campus. The gender of each student is an example of a(n) ____________________ variable. 23. The Dean of Students conducted a survey on campus. Class rank (Freshman, Sophomore, Junior, and Senior) is an example of a(n) ____________________ variable. 24. The final grade received in an English course (A, B, C, D, or F) is an example of a(n) ____________________ variable. 25. In purchasing a used automobile, there are a number of variables to consider. The age of the car is an example of a(n) ____________________ variable. 26. In purchasing an automobile, there are a number of variables to consider. The body style of the car (sedan, coupe, wagon, etc.) is an example of a(n) ____________________ variable. Assignments: 1. At the end of a tour vacation, the travel agent asks the vacationers to respond to the questions listed below. For each question, determine whether the possible responses are interval, nominal, or ordinal. a. How many tour vacations have you taken prior to this one? b. Do you feel that your tour vacation lasted sufficiently long (yes/no)? c. Which of the following features of the hotel accommodations did you find most attractive: location, facilities, room size, service, or price? d. What is the maximum number of hours per day that you would like to spend traveling? e. Is your overall rating of this tour: excellent, good, fair, or poor? 2. Before leaving a particular restaurant, customers are asked to respond to the questions listed below. For each question, determine whether the possible responses are interval, nominal, or ordinal. a. What is the approximate distance (in miles) between this restaurant and your residence? b. Have you ever eaten at this restaurant before? c. On how many occasions have you eaten at the restaurant before? d. Which of the following attributes of this restaurant do you find most attractive: service, prices, quality of the food, or the menu? e. What is your overall rating of the restaurant: excellent, good, fair, or poor? 3. For each of the following examples, identify the data type as nominal, ordinal, or interval. a. The final grade received by a student in a computer science class. b. The number of students in a statistics course. c. The starting salary of an MBA graduate. d. The size of an order of fries (small, medium, large, super-size) purchased by a McDonald's customer. e. The college you are enrolled in (Arts and Sciences, Business, Education, etc.). 4. For each of the following, indicate whether the variable of interest is nominal or interval. a. Whether you are a U.S. citizen. b. Your marital status. c. The number of cars parked in a certain parking lot at any given time. d. The amount of time you spent last week on your homework. e. Lily's travel time from her dorm to the student union on campus. f. Heidi's favorite brand of tennis balls. 5. Provide one example of nominal data; one example of ordinal data; and one example of interval data. Session 3 – Graphical Techniques Ratio/Interval Nominal Data Data Histogram Frequency and Single Set of Relative Frequency Data Tables, Bar and Pie Charts Relationship Scatter Diagram Cross-classification Between Table, Bar Charts Two Variables Multiple Choice Questions 1. Which of the following statements about pie charts is false? a. A pie chart is a graphical representation of a relative frequency distribution. b. You can always determine frequencies for each category by looking at a pie chart. c. The total percentage of all the slices of a pie chart is 100%. d. The area of a slice of a pie chart is the proportion of all the individuals that fall into that particular category. 2. Which of the following situations is best suited for a pie chart? a. The number of dollars spent this year on each type of legal gambling. b. The percentage of a charitable donation that goes to administrative costs vs. directly to the charity. c. The number of students in your class who received an A, B, C, D, F on their exam. d. All of these choices are true. 3. Which situation identifies when to use pie charts and/or bar charts? a. You want to describe a single set of data. b. Your data is nominal. c. You want to show the number or the percentage of individuals in each category. d. All of these choices are true. 4. Suppose you measure the number of minutes it takes an employee to complete a task, where the maximum allowed time is 5 minutes, and each time is rounded to the nearest minute. Data from 130 employees is summarized below. How long did it take most employees to complete the task? Time (minutes) 1 2 3 4 5 Frequency 15 30 40 25 20 a. 5 minutes b. 3 minutes c. 40 minutes d. 20 minutes 5.Car buyers were asked to indicate the car dealer they believed offered the best overall service. The four choices were Carriage Motors (C), Marco Chrysler (M), Triangle Auto (T), and University Chevrolet (U). The following data were obtained: T C C C U C M T C U U M C M T C M M C M T C C T U M M C C T T U C U T M M C U T What percentage of car buyers identified Carriage Motors as having the best overall service? a. 1/4 = 0.25 or 25% b. 14/40 = 0.35 or 35% c. 14% d. None of these choices. TRUE/FALSE 6. A bar chart is used to represent interval data. 7. One of the advantages of a pie chart is that it clearly shows that the total percentages of all the categories add to 100%. 8. Bar and pie charts are graphical techniques for nominal data. The former focus the attention on the frequency of the occurrences of each category, and the later emphasizes the proportion of occurrences of each category. 9. A relative frequency distribution lists the categories and their counts. 10. A frequency distribution lists the categories and the proportion with which each occurs. 11. From a pie chart you are able to find the frequency for each category. COMPLETION 12. Two types of graphs that organize nominal data are ____________________ and ____________________. 13. A bar chart is used to represent ____________________ data. 14. A pie chart is used to represent ____________________ data. 15. A(n) ____________________ chart is often used to display frequencies; a(n) ____________________ chart graphically shows relative frequencies. 16. A pie chart shows the ____________________ of individuals that fall into each category. 17. We can summarize nominal data in a table that presents the categories and their counts. This table is called a(n) ____________________ distribution. 18. A(n) ____________________ distribution lists the categories of a nominal variable and the proportion with which each occurs. 19. A(n) ____________________ chart is not able to show frequencies. It can only show relative frequencies. 20. In a pie chart, each slice is proportional to the ____________________ of individuals in that category. 21. A category in a pie chart that contains 25% of the observations is represented by a slice of the pie that is equal to ____________________ degrees. Assignments: 1. Identify the appropriate type of data for each of the following graphs is. a. Pie chart b. Bar chart 2. Twenty-five voters participating in a recent election exit poll in Minnesota were asked to state their political party affiliation. Coding the data as 1 for Republican, 2 for Democrat, and 3 for Independent, the data collected were as follows: 3, 1, 2, 3, 1, 3, 3, 2, 1, 3, 3, 2, 1, 1, 3, 2, 3, 1, 3, 2, 3, 2, 1, 1, and 3. Construct a frequency bar chart from this data. What does the bar chart tell you about the political affiliations of those in this sample? 3.Car Buyers Forty car buyers were asked to indicate which car dealer offered the best overall service. The four choices were Carriage Motors (C), Marco Chrysler (M), Triangle Auto (T), and University Chevrolet (U). The following data were obtained: T C C C U C M T C U U M C M T C M M C M T C C T U M M C C T T U C U T M M C U T a. {Car Buyers Narrative} Construct a frequency bar chart of this data. Which car dealer came in last place in terms of overall service? b. {Car Buyers Narrative} Construct a pie chart of this data. Which car dealer offered the best overall service? 4. Suppose you measure the number of minutes it takes an employee to complete a task, where the maximum allowed time is 5 minutes, and each time is rounded to the nearest minute. Data from 130 employees is summarized below. Construct a frequency bar chart and a pie chart from this data. How long did it take most employees to complete the task? Time (minutes) 1 2 3 4 5 Frequency 15 30 40 25 20 5. Business School Graduates A sample of business school graduates were asked what their major was. The results are shown in the following frequency distribution. Major of Graduates Number of graduates Accounting 58 Finance 42 Management 38 Marketing 52 Other 10 a. {Business School Graduates Narrative} How many graduates were surveyed? b. {Business School Graduates Narrative} Draw a pie chart to summarize this data. Which major was the most popular? c. {Business School Graduates Narrative} If you were only given the frequency bar chart below, would you able to reconstruct the original observations in the data set? d. {Business School Graduates Narrative} Draw a pie chart of this data. Are you able to reconstruct the original data from this pie chart alone?