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1、Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-1,Chapter 2 Presenting Data in Tables and Charts,Business Statistics: A First Course Fifth Edition,Choice Is Yours, Part 1,Choice Is Yours, Part 1,Comparing the Performance of Mutual Funds,Business Statistics: A First Course, 5e
2、 2009 Prentice-Hall, Inc.,Chap 2-5,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 2-6,C
3、ategorical Data Are Summarized By Tables & Graphs,Categorical Data,Graphing Data,Pie Charts,Pareto Chart,Bar Charts,Tabulating Data,Summary Table,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-7,Organizing Categorical Data: Summary Table,A summary table indicates the frequen
4、cy, amount, or percentage of items in a set of categories so that you can see differences between categories. A summary table based on a survey for banking preference,Example,The 868 mutual funds are classified according to their risk level, categorized as low, average, and high. Table 2.2,Business
5、Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-9,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.,Ch
6、ap 2-10,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.,Example,Bar Chart for the levels of risk of mutual funds (based on the information in table 2.2 ),Business S
7、tatistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-12,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.,Example,A pie chart for the levels
8、 of risk of mutual funds. See table 2.2,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-14,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
9、 polygon is shown in the same graph Used to separate the “vital few” from the “trivial many”,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-15,Organizing Categorical Data: Pareto Chart,A large injection-molding company manufacturing plastic components used in computer keyboa
10、rds. Data in Table 2.3 consist of all computer keyboards with defects produced during a three-month period.,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-16,Organizing Categorical Data: Pareto Chart,A summary table for computer keyboard data in which the categories are orde
11、red based on the frequency of defects present.,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-17,Organizing Categorical Data: Pareto Chart,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-18,Organizing Categorical Data: Pareto Chart,Business Statistics
12、: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-19,Tables and Charts for Numerical Data,Numerical Data,Ordered Array,Stem-and-Leaf Display,Histogram,Polygon,Ogive,Frequency Distributions and Cumulative Distributions,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-20,Orga
13、nizing 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),Example,A study that compares the cost of a restaurant meal in an u
14、rban area to the cost of a similar meal in the suburbs outside the city.,Example,From table 2.6 you can see that the cost of a meal at the urban restaurant is between $16 and $ 74 and the cost of a meal at the suburban restaurants is between $20 and $68.,Business Statistics: A First Course, 5e 2009
15、Prentice-Hall, Inc.,Chap 2-23,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 Prenti
16、ce-Hall, Inc.,Chap 2-24,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.,Stem and Leaf Display,Age of College Students Day Students Night Students,
17、One measure of past performance,The return of low-risk mutual funds in 2006,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-27,Organizing Numerical Data: Frequency Distribution,The frequency distribution is a summary table in which the data are arranged into numerically order
18、ed 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. .,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,
19、Chap 2-28,Organizing Numerical Data: Frequency Distribution,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 w
20、idth of a class interval, you divide the range (Highest valueLowest value) of the data by the number of class groupings desired.,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-29,Organizing Numerical Data: Frequency Distribution Example,Example: A manufacturer of insulation
21、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 2-30,Organizing Numerical Data: Frequency Distribution Example,Sort raw data in
22、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),Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Cha
23、p 2-31,Organizing Numerical Data: Frequency Distribution Example,Determine class boundaries (limits): Class 1: 10 to less than 20 Class 2: 20 to less than 30 Class 3: 30 to less than 40 Class 4: 40 to less than 50 Class 5: 50 to less than 60 Compute class midpoints: 15, 25, 35, 45, 55 Count observat
24、ions & assign to classes,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-32,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,Business Statistics: A First Course, 5e
25、2009 Prentice-Hall, Inc.,Chap 2-33,Tabulating Numerical Data: Cumulative Frequency,Class,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,Percentage,Cumulative Percentage,Data in ord
26、ered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58,Frequency,Cumulative Frequency,Example,Frequency distributions of the cost per meal of 50 urban restaurants and 50 suburban restaurants,Percentage Distribution,Cumulative Percentage Distribution,Cumulative Per
27、centage Distribution,Frequency Distribution,Relative Frequency Distribution,Cumulative Percentage Distribution,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-41,Why Use a Frequency Distribution?,It condenses the raw data into a more useful form It allows for a quick visual i
28、nterpretation 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 2-42,Frequency Distributions: Some Tips,Different class boundaries may provi
29、de 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 o
30、r 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 2-43,Organizing Numerical Data: The Histogram,A vertical bar chart of the data in a frequency distribution is called
31、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
32、.,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-44,Organizing Numerical Data: The Histogram,Daily High Temperature,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-45,Organizing Numerical Data: The Histogram,Price - Urban Restaurant,Price - Suburban R
33、estaurant,2006 Return (Growth Funds),2006 Return (Value Funds),Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-50,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 th
34、e 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, 5
35、e 2009 Prentice-Hall, Inc.,Chap 2-51,Graphing Numerical Data: The Frequency Polygon,Class,10 but less than 20 15 3 20 but less than 30 25 6 30 but less than 40 35 5 40 but less than 50 45 4 50 but less than 60 55 2,Frequency,Class Midpoint,Daily High Temperature,Business Statistics: A First Course,
36、5e 2009 Prentice-Hall, Inc.,Chap 2-52,Graphing Numerical Data: The Frequency Polygon,Percentage Polygon Cost of Meals at Urban and Suburban Restaurant,Percentage Polygon for Growth and Value Funds,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-55,Graphing Cumulative Frequenc
37、ies: The Ogive (Cumulative % Polygon),Class,10 but less than 20 10 15 20 but less than 30 20 45 30 but less than 40 30 70 40 but less than 50 40 90 50 but less than 60 50 100,% less than Lower boundary,Lower class boundary,Lower Class Boundary,Business Statistics: A First Course, 5e 2009 Prentice-Ha
38、ll, Inc.,Chap 2-56,Graphing Cumulative Frequencies: The Ogive (Cumulative % Polygon),Lower Class Boundary,Cumulative Percentage Polygon for Cost of Meals,Cumulative Percentage Polygon for Growth and Value Funds,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-59,Cross Tabulati
39、ons,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 2-60,Cross Tabulations: The Contingency Table,A cross-classification (or contingency) ta
40、ble 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 r
41、epresents the data corresponding to that specific pairing of row and column categories.,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-61,Cross Tabulations: The Contingency Table,A survey was conducted to study the importance of brand name to consumers as compared to a few y
42、ears ago. The results, classified by gender, were as follows:,Example,Pattern or relationship between the level of risk and the objective of all 868 mutual funds.,Example,Fund objective and fund risk, based on percentage of overall total.,Example,Business Statistics: A First Course, 5e 2009 Prentice
43、-Hall, Inc.,Chap 2-65,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 relati
44、onships between two numerical variables,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-66,Scatter Plot Example,Example,Relationship between the cost of fast-food meal and two movie tickets in various cities.,Example,Scatter Plot of the cost of a fast-food meal and the cost o
45、f two movie tickets.,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-69,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 ho
46、rizontal axis,Time Series Plot,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-70,Time Series Plot Example,Example,Time series plot for movie attendance, in billions, from 1999 to 2006.,Example,Time series plot for movie attendance, in billions, from 1999 to 2006.,Business St
47、atistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-73,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 pro
48、perly 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 2-74,Graphical Errors: Chart Junk,Minimum Wage,0,2,4,1960,1970,1980,1990,$,Good Presentation,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 2-75,Graphical Errors: No Relative Basis,As received by students.,As received b