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Basic Business Statistics (8th Edition) Introduction and Data Collection © 2002 Prentice-Hall, Inc. Chap 1-1 Chapter Topics Why a manager needs to know about statistics The growth and development of modern statistics Key definitions Descriptive versus inferential statistics Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-2 Chapter Topics Why data are needed Types of data and their sources Design of survey research Types of sampling methods Types of survey errors Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. (continued) Chap 1-3 Why a Manager Needs to Know about Statistics To know how to properly present information To know how to draw conclusions about populations based on sample information To know how to improve processes To know how to obtain reliable forecasts Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-4 The Growth and Development of Modern Statistics Needs of government to collect data on its citizens The development of the mathematics of probability theory The advent of the computer Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-5 Key Definitions A population (universe) is the collection of things under consideration A sample is a portion of the population selected for analysis A parameter is a summary measure computed to describe a characteristic of the population A statistic is a summary measure computed to describe a characteristic of the sample Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-6 Population and Sample Population Sample Use statistics to summarize features Use parameters to summarize features Inference on the population from the sample Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-7 Statistical Methods Descriptive statistics Collecting and describing data Inferential statistics Drawing conclusions and/or making decisions concerning a population based only on sample data Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-8 Descriptive Statistics Collect data Present data e.g. Survey e.g. Tables and graphs Characterize data e.g. Sample mean = Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. X i n Chap 1-9 Inferential Statistics Estimation e.g.: Estimate the population mean weight using the sample mean weight Hypothesis testing e.g.: Test the claim that the population mean weight is 120 pounds Drawing conclusions and/or making decisions concerning a population based on sample results. Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-10 Why We Need Data To provide input to survey To provide input to study To measure performance of service or production process To evaluate conformance to standards To assist in formulating alternative courses of action To satisfy curiosity Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-11 Data Sources Primary Secondary Data Collection Data Compilation Print or Electronic Observation Survey Experimentation Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-12 Types of Data Data Categorical (Qualitative) Numerical (Quantitative) Discrete Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Continuous Chap 1-13 Design of Survey Research Choose an appropriate mode of response Reliable primary modes Personal interview Telephone interview Mail survey Less reliable self-selection modes (not appropriate for making inferences about the population) Television survey Internet survey Printed survey on newspapers and magazines Product or service questionnaires Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-14 Design of Survey Research (continued) Identify broad categories Formulate accurate questions List complete and non-overlapping categories that reflect the theme Make questions clear and unambiguous. Use universally-accepted definitions Test the survey Pilot test the survey on a small group of participants to assess clarity and length Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-15 Design of Survey Research (continued) Write a cover letter State the goal and purpose of the survey Explain the importance of a response Provide assurance of respondent’s anonymity Offer incentive gift for respondent participation Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-16 Reasons for Drawing a Sample Less time consuming than a census Less costly to administer than a census Less cumbersome and more practical to administer than a census of the targeted population Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-17 Types of Sampling Methods Samples Non-Probability Samples Probability Samples Simple Random Judgement Chunk Quota Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Stratified Cluster Systematic Chap 1-18 Probability Sampling Subjects of the sample are chosen based on known probabilities Probability Samples Simple Random Systematic Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Stratified Cluster Chap 1-19 Simple Random Samples Every individual or item from the frame has an equal chance of being selected Selection may be with replacement or without replacement Samples obtained from table of random numbers or computer random number generators Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-20 Systematic Samples Decide on sample size: n Divide frame of N individuals into groups of k individuals: k=n/n Randomly select one individual from the 1st group Select every k-th individual thereafter N = 64 n=8 First Group k=8 Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-21 Stratified Samples Population divided into two or more groups according to some common characteristic Simple random sample selected from each group The two or more samples are combined into one Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-22 Cluster Samples Population divided into several “clusters,” each representative of the population Simple random sample selected from each The samples are combined into one Population divided into 4 clusters. Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-23 Advantages and Disadvantages Simple random sample and systematic sample Stratified sample Simple to use May not be a good representation of the population’s underlying characteristics Ensures representation of individuals across the entire population Cluster sample More cost effective Less efficient (need larger sample to acquire the same level of precision) Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-24 Evaluating Survey Worthiness What is the purpose of the survey? Is the survey based on a probability sample? Coverage error – appropriate frame Nonresponse error – follow up Measurement error – good questions elicit good responses Sampling error – always exists Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-25 Types of Survey Errors Coverage error Excluded from frame. Non response error Follow up on non responses. Sampling error Measurement error Chance differences from sample to sample. Bad Question! Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-26 Chapter Summary Addressed why a manager needs to know about statistics Discussed the growth and development of modern statistics Addressed the notion of descriptive versus inferential statistics Discussed the importance of data Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-27 Chapter Summary (continued) Defined and described the different types of data and sources Discussed the design of survey Discussed types of sampling methods Described different types of survey errors Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc. Chap 1-28 Basic Business Statistics (8th Edition) Presenting Data in Tables and Charts © 2002 Prentice-Hall, Inc. Chap 2-29 Chapter Topics Organizing numerical data Tabulating and graphing Univariate numerical data The ordered array and stem-leaf display Frequency distributions: tables, histograms, polygons Cumulative distributions: tables, the Ogive Graphing Bivariate numerical data © 2002 Prentice-Hall, Inc. Chap 2-30 Chapter Topics Tabulating and graphing Univariate categorical data The summary table Bar and pie charts, the Pareto diagram (continued) Tabulating and graphing Bivariate categorical data Contingency tables Side by side bar charts Graphical excellence and common errors in presenting data © 2002 Prentice-Hall, Inc. Chap 2-31 Organizing Numerical Data Numerical Data Ordered Array 21, 24, 24, 26, 27, 27, 30, 32, 38, 41 Stem and Leaf Display © 2002 Prentice-Hall, Inc. 2 144677 3 028 4 1 41, 24, 32, 26, 27, 27, 30, 24, 38, 21 Frequency Distributions Cumulative Distributions Histograms Tables Ogive Polygons Chap 2-32 Organizing Numerical Data (continued) Data in raw form (as collected): 24, 26, 24, 21, 27, 27, 30, 41, 32, 38 Data in ordered array from smallest to largest: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41 Stem-and-leaf display: 2 144677 3 028 4 1 © 2002 Prentice-Hall, Inc. Chap 2-33 Tabulating and Graphing Numerical Data Numerical Data Ordered Array 21, 24, 24, 26, 27, 27, 30, 32, 38, 41 41, 24, 32, 26, 27, 27, 30, 24, 38, 21 Frequency Distributions Cumulative Distributions O g ive 120 100 80 60 40 20 0 10 Stem and Leaf Display 2 144677 3 028 4 1 Histograms 30 40 50 60 Ogive 7 6 5 4 Tables Polygons 3 2 1 0 10 © 2002 Prentice-Hall, Inc. 20 20 30 40 50 60 Chap 2-34 Tabulating Numerical Data: Frequency Distributions Sort raw data in ascending order: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Find range: 58 - 12 = 46 Select number of classes: 5 (usually between 5 and 15) Compute class interval (width): 10 (46/5 then round up) Determine class boundaries (limits): Compute class midpoints: Count observations & assign to classes © 2002 Prentice-Hall, Inc. 10, 20, 30, 40, 50, 60 15, 25, 35, 45, 55 Chap 2-35 Frequency Distributions, Relative Frequency Distributions and Percentage Distributions Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Class 10 but under 20 20 but under 30 30 but under 40 40 but under 50 50 but under 60 Total © 2002 Prentice-Hall, Inc. Relative Frequency Frequency Percentage 3 6 5 4 2 20 .15 .30 .25 .20 .10 1 15 30 25 20 10 100 Chap 2-36 Graphing Numerical Data: The Histogram Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Frequency Histogram 7 6 5 4 3 2 1 0 6 5 3 2 0 5 Class Boundaries © 2002 Prentice-Hall, Inc. No Gaps Between Bars 4 0 15 25 36 45 Class Midpoints 55 More Chap 2-37 Graphing Numerical Data: The Frequency Polygon Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Frequenc y 7 6 5 4 3 2 1 0 5 © 2002 Prentice-Hall, Inc. 15 25 36 45 55 Class Midpoints M ore Chap 2-38 Tabulating Numerical Data: Cumulative Frequency Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Class 10 but under 20 20 but under 30 30 but under 40 40 but under 50 50 but under 60 © 2002 Prentice-Hall, Inc. Cumulative Frequency 3 9 14 18 20 Cumulative % Frequency 15 45 70 90 100 Chap 2-39 Graphing Numerical Data: The Ogive (Cumulative % Polygon) Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Ogive 100 80 60 40 20 0 10 20 30 40 50 60 Class Boundaries (Not Midpoints) © 2002 Prentice-Hall, Inc. Chap 2-40 Graphing Bivariate Numerical Data (Scatter Plot) Mutual Funds Scatter Plot Total Year to Date Return (%) 40 30 20 10 0 0 © 2002 Prentice-Hall, Inc. 10 20 30 Net Asset Values 40 Chap 2-41 Tabulating and Graphing Categorical Data:Univariate Data Categorical Data Tabulating Data The Summary Table Graphing Data Pie Charts Bar Charts © 2002 Prentice-Hall, Inc. Pareto Diagram Chap 2-42 Summary Table (for an Investor’s Portfolio) Investment Category Amount Percentage (in thousands $) Stocks Bonds CD Savings Total 46.5 32 15.5 16 110 42.27 29.09 14.09 14.55 100 Variables are Categorical © 2002 Prentice-Hall, Inc. Chap 2-43 Graphing Categorical Data: Univariate Data Categorical Data Graphing Data Tabulating Data The Summary Table Pie Charts CD Pareto Diagram S a vi n g s Bar Charts B onds S to c k s 0 10 20 30 40 50 45 120 40 100 35 30 80 25 60 20 15 40 10 20 5 0 0 S to c k s © 2002 Prentice-Hall, Inc. B onds S a vi n g s CD Chap 2-44 Bar Chart (for an Investor’s Portfolio) Investor's Portfolio Savings CD Bonds Stocks 0 10 20 30 40 50 Amount in K$ © 2002 Prentice-Hall, Inc. Chap 2-45 Pie Chart (for an Investor’s Portfolio) Amount Invested in K$ Savings 15% Stocks 42% CD 14% Bonds 29% © 2002 Prentice-Hall, Inc. Percentages are rounded to the nearest percent. Chap 2-46 Pareto Diagram Axis for bar chart shows % invested in each category 45% 100% 40% 90% 80% 35% 70% 30% 60% 25% 50% 20% 40% 15% 30% 10% 20% 5% 10% 0% 0% Stocks © 2002 Prentice-Hall, Inc. Bonds Savings Axis for line graph shows cumulative % invested CD Chap 2-47 Tabulating and Graphing Bivariate Categorical Data Contingency tables: Investment Category Investor A Stocks Bonds CD Savings 46.5 32 15.5 16 Total 110 © 2002 Prentice-Hall, Inc. investment in thousands of dollars Investor B Investor C Total 55 44 20 28 27.5 19 13.5 7 129 95 49 51 147 67 324 Chap 2-48 Tabulating and Graphing Bivariate Categorical Data Side by side charts C o m p arin g In vesto rs S avings CD B onds S toc k s 0 10 Inves tor A © 2002 Prentice-Hall, Inc. 20 30 Inves tor B 40 50 60 Inves tor C Chap 2-49 Principles of Graphical Excellence Presents data in a way that provides substance, statistics and design Communicates complex ideas with clarity, precision and efficiency Gives the largest number of ideas in the most efficient manner Almost always involves several dimensions Tells the truth about the data © 2002 Prentice-Hall, Inc. Chap 2-50 Errors in Presenting Data Using “chart junk” Failing to provide a relative basis in comparing data between groups Compressing the vertical axis Providing no zero point on the vertical axis © 2002 Prentice-Hall, Inc. Chap 2-51 “Chart Junk” Bad Presentation Good Presentation Minimum Wage 1960: $1.00 Minimum Wage 4 $ 1970: $1.60 2 1980: $3.10 0 1990: $3.80 © 2002 Prentice-Hall, Inc. 1960 1970 1980 1990 Chap 2-52 No Relative Basis Bad Presentation Good Presentation A’s received by Freq. students. 300 200 30 % 10 0 FR SO JR SR A’s received by students. FR SO JR SR FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior © 2002 Prentice-Hall, Inc. Chap 2-53 Compressing Vertical Axis Bad Presentation Good Presentation Quarterly Sales 200 $ Quarterly Sales 50 100 25 0 0 Q1 Q2 © 2002 Prentice-Hall, Inc. Q3 Q4 $ Q1 Q2 Q3 Q4 Chap 2-54 No Zero Point on Vertical Axis Bad Presentation Good Presentation Monthly Sales 45 $ Monthly Sales 42 39 45 42 39 $ 36 36 J F M A M J 0 J F M A M J Graphing the first six months of sales. © 2002 Prentice-Hall, Inc. Chap 2-55 Chapter Summary Organized numerical data Tabulated and graphed univariate numerical data The ordered array and stem-leaf display Frequency distributions: tables, histograms, polygon Cumulative distributions: tables and the Ogive Graphed bivariate numerical data © 2002 Prentice-Hall, Inc. Chap 2-56 Chapter Summary Tabulated and graphed univariate categorical data The summary table Bar and pie charts, the Pareto diagram Tabulated and graphed bivariate categorical data (continued) Contingency tables Side by side charts Discussed graphical excellence and common errors in presenting data © 2002 Prentice-Hall, Inc. Chap 2-57 Basic Business Statistics (8th Edition) Numerical Descriptive Measures © 2002 Prentice-Hall, Inc. Chap 3-58 Chapter Topics Measures of central tendency Mean, median, mode, geometric mean, midrange Quartile Measure of variation Range, Interquartile range, variance and standard deviation, coefficient of variation Shape Symmetric, skewed, using box-and-whisker plots © 2002 Prentice-Hall, Inc. Chap 3-59 Chapter Topics (continued) Coefficient of correlation Pitfalls in numerical descriptive measures and ethical considerations © 2002 Prentice-Hall, Inc. Chap 3-60 Summary Measures Summary Measures Central Tendency Mean Quartile Mode Median Range Variation Coefficient of Variation Variance Geometric Mean © 2002 Prentice-Hall, Inc. Standard Deviation Chap 3-61 Measures of Central Tendency Central Tendency Average Median Mode n X X i 1 N i 1 Geometric Mean X G X1 X 2 n X i Xn 1/ n i N © 2002 Prentice-Hall, Inc. Chap 3-62 Mean (Arithmetic Mean) Mean (arithmetic mean) of data values Sample mean Sample Size n X X i 1 i n Xn Population mean Population Size N © 2002 Prentice-Hall, Inc. X1 X 2 n X i 1 N i X1 X 2 N XN Chap 3-63 Mean (Arithmetic Mean) (continued) The most common measure of central tendency Affected by extreme values (outliers) 0 1 2 3 4 5 6 7 8 9 10 Mean = 5 © 2002 Prentice-Hall, Inc. 0 1 2 3 4 5 6 7 8 9 10 12 14 Mean = 6 Chap 3-64 Median Robust measure of central tendency Not affected by extreme values 0 1 2 3 4 5 6 7 8 9 10 Median = 5 0 1 2 3 4 5 6 7 8 9 10 12 14 Median = 5 In an ordered array, the median is the “middle” number If n or N is odd, the median is the middle number If n or N is even, the median is the average of the two middle numbers © 2002 Prentice-Hall, Inc. Chap 3-65 Mode A measure of central tendency Value that occurs most often Not affected by extreme values Used for either numerical or categorical data There may may be no mode There may be several modes 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mode = 9 © 2002 Prentice-Hall, Inc. 0 1 2 3 4 5 6 No Mode Chap 3-66 Geometric Mean Useful in the measure of rate of change of a variable over time X G X1 X 2 Xn 1/ n Geometric mean rate of return Measures the status of an investment over time RG 1 R1 1 R2 © 2002 Prentice-Hall, Inc. 1 Rn 1/ n 1 Chap 3-67 Example An investment of $100,000 declined to $50,000 at the end of year one and rebounded to $100,000 at end of year two: X1 $100,000 X 2 $50,000 X 3 $100,000 Average rate of return: (50%) (100%) X 25% 2 Geometric rate of return: RG 1 50% 1 100% 1/ 2 0.50 2 1/ 2 © 2002 Prentice-Hall, Inc. 1 1 1 1 0% 1/ 2 Chap 3-68 Quartiles Split Ordered Data into 4 Quarters 25% 25% Q1 25% Q2 Position of i-th Quartile 25% Q3 i n 1 Qi 4 Data in Ordered Array: 11 12 13 16 16 17 18 21 22 1 9 1 Position of Q1 2.5 4 Q1 12 13 12.5 2 Q1 and Q3 Are Measures of Noncentral Location Q = Median, A Measure of Central Tendency 2 © 2002 Prentice-Hall, Inc. Chap 3-69 Measures of Variation Variation Variance Range Population Variance Sample Variance Interquartile Range © 2002 Prentice-Hall, Inc. Standard Deviation Coefficient of Variation Population Standard Deviation Sample Standard Deviation Chap 3-70 Range Measure of variation Difference between the largest and the smallest observations: Range X Largest X Smallest Ignores the way in which data are distributed Range = 12 - 7 = 5 Range = 12 - 7 = 5 7 8 © 2002 Prentice-Hall, Inc. 9 10 11 12 7 8 9 10 11 12 Chap 3-71 Interquartile Range Measure of variation Also known as midspread Spread in the middle 50% Difference between the first and third quartiles Data in Ordered Array: 11 12 13 16 16 17 17 18 21 Interquartile Range Q3 Q1 17.5 12.5 5 Not affected by extreme values © 2002 Prentice-Hall, Inc. Chap 3-72 Variance Important measure of variation Shows variation about the mean Sample variance: n S 2 X i 1 X i 2 n 1 Population variance: N 2 © 2002 Prentice-Hall, Inc. X i 1 i N 2 Chap 3-73 Standard Deviation Most important measure of variation Shows variation about the mean Has the same units as the original data Sample standard deviation: n S Population standard deviation: © 2002 Prentice-Hall, Inc. X i 1 X i 2 n 1 N X i 1 i 2 N Chap 3-74 Comparing Standard Deviations Data A 11 12 13 14 15 16 17 18 19 20 21 Mean = 15.5 s = 3.338 Data B 11 12 13 14 15 16 17 18 19 20 21 Mean = 15.5 s = .9258 Data C 11 12 13 14 15 16 17 18 19 20 21 © 2002 Prentice-Hall, Inc. Mean = 15.5 s = 4.57 Chap 3-75 Coefficient of Variation Measures relative variation Always in percentage (%) Shows variation relative to mean Is used to compare two or more sets of data measured in different units S CV X © 2002 Prentice-Hall, Inc. 100% Chap 3-76 Comparing Coefficient of Variation Stock A: Stock B: Average price last year = $50 Standard deviation = $5 Average price last year = $100 Standard deviation = $5 Coefficient of variation: Stock A: Stock B: © 2002 Prentice-Hall, Inc. S CV X $5 100% 100% 10% $50 S CV X $5 100% 100% 5% $100 Chap 3-77 Shape of a Distribution Describes how data is distributed Measures of shape Symmetric or skewed Left-Skewed Mean < Median < Mode © 2002 Prentice-Hall, Inc. Symmetric Mean = Median =Mode Right-Skewed Mode < Median < Mean Chap 3-78 Exploratory Data Analysis Box-and-whisker plot Graphical display of data using 5-number summary X smallest Q 1 4 © 2002 Prentice-Hall, Inc. 6 Median( Q2) 8 Q3 10 Xlargest 12 Chap 3-79 Distribution Shape and Box-and-Whisker Plot Left-Skewed Q1 © 2002 Prentice-Hall, Inc. Q2 Q3 Symmetric Q1Q2Q3 Right-Skewed Q1 Q2 Q3 Chap 3-80 Coefficient of Correlation Measures the strength of the linear relationship between two quantitative variables n r X i 1 n X i 1 © 2002 Prentice-Hall, Inc. i i X Yi Y X 2 n Y Y i 1 2 i Chap 3-81 Features of Correlation Coefficient Unit free Ranges between –1 and 1 The closer to –1, the stronger the negative linear relationship The closer to 1, the stronger the positive linear relationship The closer to 0, the weaker any positive linear relationship © 2002 Prentice-Hall, Inc. Chap 3-82 Scatter Plots of Data with Various Correlation Coefficients Y Y Y X r = -1 X r = -.6 Y © 2002 Prentice-Hall, Inc. X r=0 Y r = .6 X r=1 X Chap 3-83 Pitfalls in Numerical Descriptive Measures Data analysis is objective Should report the summary measures that best meet the assumptions about the data set Data interpretation is subjective Should be done in fair, neutral and clear manner © 2002 Prentice-Hall, Inc. Chap 3-84 Ethical Considerations Numerical descriptive measures: Should document both good and bad results Should be presented in a fair, objective and neutral manner Should not use inappropriate summary measures to distort facts © 2002 Prentice-Hall, Inc. Chap 3-85 Chapter Summary Described measures of central tendency Mean, median, mode, geometric mean, midrange Discussed quartile Described measure of variation Range, interquartile range, variance and standard deviation, coefficient of variation Illustrated shape of distribution Symmetric, skewed, box-and-whisker plots © 2002 Prentice-Hall, Inc. Chap 3-86 Chapter Summary (continued) Discussed correlation coefficient Addressed pitfalls in numerical descriptive measures and ethical considerations © 2002 Prentice-Hall, Inc. Chap 3-87