Business Statistics: A First Course Fifth Edition Chapter 2 PDF

Business Statistics: A First Course Fifth Edition Chapter 2 Presenting Data in Tables and Charts B...

Business Statistics: A First Course Fifth Edition Chapter 2 Presenting Data in Tables and Charts Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-1  Learning Objectives In this chapter you learn: To develop tables and charts for categorical data To develop tables and charts for numerical data The principles of properly presenting graphs Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-2  Categorical Data Are Summarized By Tables & Graphs Categorical Data Tabulating Data Graphing Data Summary Bar Pie Pareto Table Charts Charts Chart Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-3  Organizing Categorical Data: Summary Table  A summary table indicates the frequency, amount, or percentage of items in a set of categories so that you can see differences between categories. Banking Preference? Percent ATM 16% Automated or live telephone 2% Drive-through service at branch 17% In person at branch 41% Internet 24% Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-4  Bar and Pie Charts Bar charts and Pie charts are often used for categorical data Length of bar or size of pie slice shows the frequency or percentage for each category Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-5  Organizing Categorical Data: Bar Chart  In a bar chart, a bar shows each category, the length of which represents the amount, frequency or percentage of values falling into a category. Banking Preference Internet In person at branch Drive-through service at branch Automated or live telephone ATM 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-6  Organizing Categorical Data: Pie Chart  The pie chart is a circle broken up into slices that represent categories. The size of each slice of the pie varies according to the percentage in each category. (e.g., Mutual_lecture1) Banking Preference 16% ATM 24% 2% Automated or live telephone Drive-through service at 17% branch In person at branch Internet 41% Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-7  Organizing Categorical Data: Pareto Chart Used to portray categorical data (nominal scale) A vertical bar chart, where categories are shown in descending order of frequency A cumulative polygon is shown in the same graph Used to separate the “vital few” from the “trivial many” (e.g., Banking_lecture1) Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-8  Organizing Categorical Data: Pareto Chart Pareto Chart For Banking Preference 100% 100% % in each category 80% 80% Cumulative % (line graph) (bar graph) 60% 60% 40% 40% 20% 20% 0% 0% In person Internet Drive- ATM Automated at branch through or live service at telephone branch Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-9  Tables and Charts for Numerical Data Numerical Data Frequency Distributions Ordered Array and Cumulative Distributions Stem-and-Leaf Ogive Histogram Polygon Display (e.g., (e.g., Frequency cumulative frequency lines) lines) Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-10  Organizing Numerical Data: Ordered Array  An ordered array is a sequence of data, in rank order, from the smallest value to the largest value.  Shows range (minimum value to maximum value)  May help identify outliers (unusual observations) Age of Day Students Surveyed 16 17 17 18 18 18 College Students 19 19 20 20 21 22 22 25 27 32 38 42 Night Students 18 18 19 19 20 21 23 28 32 33 41 45 Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-11  Stem-and-Leaf Display A simple way to see how the data are distributed and where concentrations of data exist METHOD: Separate the sorted data series into leading digits (the stems) and the trailing digits (the leaves) Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-12  Organizing Numerical Data: Stem and Leaf Display  A stem-and-leaf display organizes data into groups (called stems) so that the values within each group (the leaves) branch out to the right on each row. Age of College Students Age of Day Students Day Students Night Students Surveyed 16 17 17 18 18 18 Stem Leaf College Stem Leaf Students 19 19 20 20 21 22 1 67788899 1 8899 22 25 27 32 38 42 Night Students 2 0012257 2 0138 18 18 19 19 20 21 3 28 3 23 23 28 32 33 41 45 4 2 4 15 Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-13  Organizing Numerical Data: Frequency Distribution  The frequency distribution is a summary table in which the data are arranged into numerically ordered classes.  You must give attention to selecting the appropriate number of class groupings for the table, determining a suitable width of a class grouping, and establishing the boundaries of each class grouping to avoid overlapping.  The number of classes depends on the number of values in the data. With a larger number of values, typically there are more classes. In general, a frequency distribution should have at least 5 but no more than 15 classes.  To determine the width of a class interval, you divide the range (Highest value–Lowest value) of the data by the number of class groupings desired. Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-14  Organizing Numerical Data: Frequency Distribution Example Example: A manufacturer of insulation randomly selects 20 winter days and records the daily high temperature 24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27 Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-15  Organizing Numerical Data: Frequency Distribution Example  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 limits (boundaries):  Class 1: 10 to less than 20 (9.5 – 19.5)  Class 2: 20 to less than 30 (19.5 – 29.5)  Class 3: 30 to less than 40  Class 4: 40 to less than 50  Class 5: 50 to less than 60  Compute class midpoints: 14.5, 24.5, 34.5, 44.5, 55.5  Count observations & assign to classes Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-16  Organizing Numerical Data: Frequency Distribution Example Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Relative Class Frequency Percentage Frequency 10 but less than 20 3.15 15 20 but less than 30 6.30 30 30 but less than 40 5.25 25 40 but less than 50 4.20 20 50 but less than 60 2.10 10 Total 20 1.00 100 Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-17  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 Cumulative Cumulative Class Frequency Percentage Frequency Percentage 10 but less than 20 3 15 3 15 20 but less than 30 6 30 9 45 30 but less than 40 5 25 14 70 40 but less than 50 4 20 18 90 50 but less than 60 2 10 20 100 Total 20 100 Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-18  Why Use a Frequency Distribution? It condenses the raw data into a more useful form It allows for a quick visual interpretation of the data It enables the determination of the major characteristics of the data set including where the data are concentrated / clustered Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-19  Frequency Distributions: Some Tips Different class boundaries may provide different pictures for the same data (especially for smaller data sets) Shifts in data concentration may show up when different class boundaries are chosen As the size of the data set increases, the impact of alterations in the selection of class boundaries is greatly reduced When comparing two or more groups with different sample sizes, you must use either a relative frequency or a percentage distribution Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-20  Organizing Numerical Data: The Histogram  A vertical bar chart of the data in a frequency distribution is called a histogram.  In a histogram there are no gaps between adjacent bars.  The class boundaries (or class midpoints) are shown on the horizontal axis.  The vertical axis is either frequency, relative frequency, or percentage.  The height of the bars represent the frequency, relative frequency, or percentage. Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-21  Organizing Numerical Data: The Histogram Relative Class Frequency Percentage Frequency 10 but less than 20 3.15 15 20 but less than 30 6.30 30 30 but less than 40 5.25 25 Histogram : Daily High Tem perature 40 but less than 50 4.20 20 7 50 but less than 60 2.10 10 Total 20 1.00 100 6 5 Frequency 4 (In a percentage histogram the vertical 3 axis would be defined to 2 show the percentage of observations per class) 1 (e.g., restaurant_lecture1) 0 5 15 25 35 45 55 More Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-22  Organizing Numerical Data: The Polygon  A percentage polygon is formed by having the midpoint of each class represent the data in that class and then connecting the sequence of midpoints at their respective class percentages.  The cumulative percentage polygon, or ogive, displays the variable of interest along the X axis, and the cumulative percentages along the Y axis.  Useful when there are two or more groups to compare. Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-23  Graphing Numerical Data: The Frequency Polygon Class Class Midpoint Frequency 10 but less than 20 15 3 20 but less than 30 25 6 30 but less than 40 35 5 Frequency Polygon: Daily High Temperature 40 but less than 50 45 4 7 50 but less than 60 55 2 6 5 Frequency 4 3 2 (In a percentage 1 polygon the vertical axis 0 would be defined to 5 15 25 35 45 55 65 show the percentage of observations per class) Class Midpoints (e.g., restaurant_lecture1) Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-24  Graphing Cumulative Frequencies: The Ogive (Cumulative % Polygon) Lower % less class than lower Class boundary boundary 10 but less than 20 10 15 20 but less than 30 20 45 30 but less than 40 30 70 Ogive: Daily High Temperature 40 but less than 50 40 90 50 but less than 60 50 100 100 Cumulative Percentage 80 60 40 (In an ogive the percentage 20 of the observations less 0 than each lower class boundary are plotted versus 10 20 30 40 50 60 the lower class boundaries. Lower Class Boundary Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-25  Cross Tabulations Used to study patterns that may exist between two or more categorical variables. Cross tabulations can be presented in Contingency Tables Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-26  Cross Tabulations: The Contingency Table  A cross-classification (or contingency) table presents the results of two categorical variables. The joint responses are classified so that the categories of one variable are located in the rows and the categories of the other variable are located in the columns.  The cell is the intersection of the row and column and the value in the cell represents the data corresponding to that specific pairing of row and column categories. Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-27  Cross Tabulations: The Contingency Table A survey was conducted to study the importance of brand name to consumers as compared to a few years ago. The results, classified by gender, were as follows: Importance of Male Female Total Brand Name More 450 300 750 Equal or Less 3300 3450 6750 Total 3750 3750 7500 Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-28  Scatter Plots  Scatter plots are used for numerical data consisting of paired observations taken from two numerical variables  One variable is measured on the vertical axis and the other variable is measured on the horizontal axis  Scatter plots are used to examine possible relationships between two numerical variables  (e.g., Cost of Living_lecture1) Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-29  Scatter Plot Example Volume Cost per Cost per Day vs. Production Volume per day day 23 125 250 26 140 200 29 146 150 Cost per Day 33 160 100 38 167 50 42 170 0 50 188 20 30 40 50 60 70 55 195 Volume per Day 60 200 Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-30  Time Series Plot A Time Series Plot is used to study patterns in the values of a numeric variable over time The Time Series Plot: Numeric variable is measured on the vertical axis and the time period is measured on the horizontal axis (e.g., movie_lecture1) Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-31  Time Series Plot Example Number of Year Franchises Number of Franchises, 1996-2004 120 1996 43 100 1997 54 Franchises 80 Number of 1998 60 60 1999 73 40 20 2000 82 0 2001 95 1994 1996 1998 2000 2002 2004 2006 2002 107 Year 2003 99 2004 95 Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-32  Principles of Excellent Graphs  The graph should not distort the data.  The graph should not contain unnecessary adornments (sometimes referred to as chart junk).  The scale on the vertical axis should begin at zero.  All axes should be properly labeled.  The graph should contain a title.  The simplest possible graph should be used for a given set of data. Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-33  Graphical Errors: Chart Junk Bad Presentation  Good Presentation Minimum Wage Minimum Wage 1960: $1.00 $ 4 1970: $1.60 2 1980: $3.10 0 1990: $3.80 1960 1970 1980 1990 Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-34  Graphical Errors: No Relative Basis Bad Presentation Good Presentation A’s received by A’s received by Freq. students. % students. 30% 300 200 20% 100 10% 0 0% FR SO JR SR FR SO JR SR FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior FR = 260/1300, SO = 150/600, JR = 180/900, SR = 200/900 Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-35  Graphical Errors: Compressing the Vertical Axis Bad Presentation  Good Presentation Quarterly Sales Quarterly Sales $ $ 200 50 100 25 0 0 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-36  Graphical Errors: No Zero Point on the Vertical Axis Bad Presentation  Good Presentations Monthly Sales $ Monthly Sales $ 45 45 42 42 39 39 36 36 0 J F M A M J J F M A M J Graphing the first six months of sales Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-37  Chapter Summary In this chapter, we have  Organized categorical data using the summary table, bar chart, pie chart, and Pareto chart.  Organized numerical data using the ordered array, stem-and- leaf display, frequency distribution, histogram, polygon, and ogive.  Examined cross tabulated data using the contingency table.  Developed scatter plots and time series graphs.  Examined the do’s and don'ts of graphically displaying data. Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 2-38