Statistics for Managers using Microsoft Excel 6th Edition Chapter 2 Organizing and Visualizing Data Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-1 Learning Objectives In this chapter you learn: The sources of data used in business The types of data used in business To develop tables and charts for numerical data To develop tables and charts for categorical data The principles of properly presenting graphs Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-2 A Step by Step Process For Examining &

Concluding From Data Is Helpful In this book we will use DCOVA Define the variables for which you want to reach conclusions Collect the data from appropriate sources Organize the data collected by developing tables Visualize the data by developing charts Analyze the data by examining the appropriate tables and charts (and in later chapters by using other statistical methods) to reach conclusions Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-3 Types of Variables DCOVA Categorical (qualitative) variables have values that can only be placed into categories, such as yes and no. Numerical (quantitative) variables have values that represent quantities. Discrete variables arise from a counting process Continuous variables arise from a measuring process

Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-4 Types of Variables DCOVA Variables Categorical Numerical Examples: Marital Status Political Party Eye Color (Defined categories) Discrete Examples: Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall Number of Children Defects per hour (Counted items) Continuous Examples:

Weight Voltage (Measured characteristics) 2-5 Levels of Measurement DCOVA A nominal scale classifies data into distinct categories in which no ranking is implied. Categorical Variables Categories Personal Computer Ownership Yes / No Type of Stocks Owned Growth / Value / Other Internet Provider Microsoft Network / AOL/ Other Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-6 Levels of Measurement (cont.) DCOVA An ordinal scale classifies data into distinct categories in which ranking is implied Categorical Variable Ordered Categories Student class designation

Freshman, Sophomore, Junior, Senior Product satisfaction Satisfied, Neutral, Unsatisfied Faculty rank Professor, Associate Professor, Assistant Professor, Instructor Standard & Poors bond ratings AAA, AA, A, BBB, BB, B, CCC, CC, C, DDD, DD, D Student Grades A, B, C, D, F Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-7 Levels of Measurement (cont.) DCOVA An interval scale is an ordered scale in which the difference between measurements is a meaningful quantity but the measurements do not have a true zero point. A ratio scale is an ordered scale in which the difference between the measurements is a

meaningful quantity and the measurements have a true zero point. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-8 Interval and Ratio Scales DCOVA Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-9 Why Collect Data? DCOVA A marketing research analyst needs to assess the effectiveness of a new television advertisement. A pharmaceutical manufacturer needs to determine whether a new drug is more effective than those currently in use. An operations manager wants to monitor a manufacturing process to find out whether the quality of the product being manufactured is conforming to company standards. An auditor wants to review the financial transactions of a company in order to determine whether the company is in compliance with generally accepted accounting principles. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall

2-10 Sources of Data DCOVA Primary Sources: The data collector is the one using the data for analysis Data from a political survey Data collected from an experiment Observed data Secondary Sources: The person performing data analysis is not the data collector Analyzing census data Examining data from print journals or data published on the internet. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-11 Sources of data fall into four categories DCOVA Data distributed by an organization or an individual A designed experiment A survey

An observational study Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-12 Examples Of Data Distributed By Organizations or Individuals DCOVA Financial data on a company provided by investment services. Industry or market data from market research firms and trade associations. Stock prices, weather conditions, and sports statistics in daily newspapers. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-13 Examples of Data From A Designed Experiment DCOVA Consumer testing of different versions of a

product to help determine which product should be pursued further. Material testing to determine which suppliers material should be used in a product. Market testing on alternative product promotions to determine which promotion to use more broadly. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-14 Examples of Survey Data DCOVA Political polls of registered voters during political campaigns. People being surveyed to determine their satisfaction with a recent product or service experience. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-15 Examples of Data From Observational Studies DCOVA

Market researchers utilizing focus groups to elicit unstructured responses to open-ended questions. Measuring the time it takes for customers to be served in a fast food establishment. Measuring the volume of traffic through an intersection to determine if some form of advertising at the intersection is justified. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-16 Categorical Data Are Organized By Utilizing Tables DCOVA Categorical Data Tallying Data One Categorical Variable Two Categorical Variables Summary

Table Contingency Table Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-17 Organizing Categorical Data: Summary Table DCOVA A summary table indicates the frequency, amount, or percentage of items in a set of categories so that you can see differences between categories. Summary Table From A Survey of 1000 Banking Customers Banking Preference? ATM Automated or live telephone Percent 16% 2% Drive-through service at branch 17% In person at branch 41% Internet 24% Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall

2-18 A Contingency Table Helps Organize Two or More Categorical Variables DCOVA Used to study patterns that may exist between the responses of two or more categorical variables Cross tabulates or tallies jointly the responses of the categorical variables For two variables the tallies for one variable are located in the rows and the tallies for the second variable are located in the columns Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-19 Contingency Table - Example DCOVA A random sample of 400 Contingency Table Showing invoices is drawn.

Frequency of Invoices Categorized Each invoice is categorized By Size and The Presence Of Errors as a small, medium, or large No Errors Errors Total amount. Small 170 20 190 Each invoice is also Amount examined to identify if there Medium 100 40 140 are any errors. Amount This data are then organized Large 65 5 70 Amount in the contingency table to the right. 335 65 400 Total Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-20 Contingency Table Based On Percentage Of Overall Total

No Errors DCOVA Errors Small Amount 170 20 190 Medium Amount 100 40 140 Large Amount 65 335 5 65 42.50% = 170 / 400 25.00% = 100 / 400 16.25% = 65 / 400 Total

No Errors 70 400 Total 83.75% of sampled invoices have no errors and 47.50% of sampled invoices are for small amounts. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall Errors Total Small Amount 42.50% 5.00% 47.50% Medium Amount 25.00% 10.00% 35.00% Large Amount

16.25% 1.25% 17.50% 83.75% 16.25% 100.0% Total 2-21 Contingency Table Based On Percentage of Row Totals No Errors DCOVA Errors Small Amount 170 20 190 Medium Amount 100

40 140 Large Amount 65 335 5 65 89.47% = 170 / 190 71.43% = 100 / 140 92.86% = 65 / 70 Total No Errors Errors Total Small Amount 89.47% 10.53% 100.0% Medium Amount 71.43%

28.57% 100.0% Large Amount 92.86% 7.14% 100.0% 83.75% 16.25% 100.0% 70 400 Total Medium invoices have a larger chance (28.57%) of having errors than small (10.53%) or large (7.14%) invoices. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall Total 2-22 Contingency Table Based On Percentage Of Column Total No Errors

DCOVA Errors Total Small Amount 170 20 190 Medium Amount 100 40 140 Large Amount 65 335 5 65 50.75% = 170 / 335 30.77% = 20 / 65 No Errors Errors

Total Small Amount 50.75% 30.77% 47.50% Medium Amount 29.85% 61.54% 35.00% Large Amount 19.40% 7.69% 17.50% 100.0% 100.0% 100.0% 70 400

Total There is a 61.54% chance that invoices with errors are of medium size. Total Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-23 Tables Used For Organizing Numerical Data DCOVA Numerical Data Ordered Array Frequency Distributions Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall Cumulative Distributions 2-24 Organizing Numerical Data: Ordered Array DCOVA 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 Surveyed College Students Day Students 16 19 22 17 19 25 17 20 27 18 20 32 18 21 38 18 22 42 19 32 19

33 20 41 21 45 Night Students 18 23 18 28 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-25 Organizing Numerical Data: Frequency Distribution DCOVA 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 valueLowest value) of the data by the number of class groupings desired. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-26 Organizing Numerical Data: Frequency Distribution Example DCOVA 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 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-27 Organizing Numerical Data: Frequency Distribution Example DCOVA 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): Class 1: Class 2: Class 3: Class 4: Class 5: 10 to less than 20 20 to less than 30 30 to less than 40 40 to less than 50 50 to less than 60 Compute class midpoints: 15, 25, 35, 45, 55 Count observations & assign to classes Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-28 Organizing Numerical Data: Frequency Distribution Example DCOVA 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 less than 20

20 but less than 30 30 but less than 40 40 but less than 50 50 but less than 60 Total Midpoints Frequency 15 25 35 45 55 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 3 6 5 4 2 20 2-29 Organizing Numerical Data: Relative & Percent Frequency Distribution Example DCOVA 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 less than 20 20 but less than 30 30 but less than 40 40 but less than 50 50 but less than 60 Total

Frequency 3 6 5 4 2 20 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall Relative Frequency .15 .30 .25 .20 .10 1.00 Percentage 15 30 25 20 10 100 2-30 Organizing Numerical Data: Cumulative Frequency Distribution Example DCOVA 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 Frequency Percentage 10 but less than 20 20 but less than 30 6 30 but less than 40 5 40 but less than 50 3 4 50 but less than 60 2 Total 20 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall Cumulative Cumulative Frequency Percentage 15% 30% 25% 20% 9 14 10% 20 100

3 18 20 15% 45% 70% 90% 100% 100% 2-31 Why Use a Frequency Distribution? DCOVA 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 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-32 Frequency Distributions: Some Tips DCOVA

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 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-33 Visualizing Categorical Data Through Graphical Displays DCOVA Categorical Data Visualizing Data Contingency Table For Two Variables Summary Table For One

Variable Bar Chart Pareto Chart Side By Side Bar Chart Pie Chart Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-34 Visualizing Categorical Data: The Bar Chart DCOVA 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 which come from the summary table of the variable. Banking Preference Banking Preference? ATM % Internet 16% 2% In person at branch

Drive-through service at branch 17% Drive-through service at branch In person at branch 41% Automated or live telephone Internet 24% Automated or live telephone ATM 0% Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 5% 10% 15% 20% 25% 30% 35% 40% 45% 2-35 Visualizing Categorical Data: The Pie Chart DCOVA 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. Banking Preference

Banking Preference? ATM Automated or live telephone % 16% 24% 2% Drive-through service at branch 17% In person at branch 41% Internet 24% ATM 16% 2% 17% Drive-through service at branch In person at branch 41%

Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall Automated or live telephone Internet 2-36 Visualizing Categorical Data: The Pareto Chart DCOVA 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 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-37 Visualizing Categorical Data: The Pareto Chart (cont) DCOVA

100% 100% 80% 80% 60% 60% 40% 40% 20% 20% 0% 0% In person Internet at branch Drivethrough service at branch Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall ATM Cumulative % (line graph) % in each category (bar graph)

Pareto Chart For Banking Preference Automated or live telephone 2-38 Visualizing Categorical Data: Side By Side Bar Charts DCOVA The side by side bar chart represents the data from a contingency table. Small Amount No Errors Errors Total 50.75% 30.77% 47.50% Medium Amount 29.85% 61.54%

35.00% Large Amount 19.40% 7.69% 17.50% 100.0% 100.0% 100.0% Total Invoice Size Split Out By Errors & No Errors Errors No Errors 0.0% 10.0% 20.0% Small 30.0% 40.0% Medium 50.0%

60.0% 70.0% Large Invoices with errors are much more likely to be of medium size (61.54% vs 30.77% and 7.69%) Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-39 Visualizing Numerical Data By Using Graphical Displays DCOVA Numerical Data Frequency Distributions and Cumulative Distributions Ordered Array Stem-and-Leaf Display Histogram Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall Polygon Ogive 2-40 Stem-and-Leaf Display

DCOVA 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) Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-41 Organizing Numerical Data: Stem and Leaf Display DCOVA 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 Surveye d College Students Day Students Day Students 16 17 17 18

18 18 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 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall Stem Leaf Night Students Stem Leaf 1 67788899 1 8899 2 0012257 2 0138

3 28 3 23 4 2 4 15 2-42 Visualizing Numerical Data: The Histogram DCOVA 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. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-43 Visualizing Numerical Data: The Histogram Frequency Relative Frequency Percentage 10 but less than 20 20 but less than 30 30 but less than 40 3 6 5 .15 .30 .25 15 30 25 40 but less than 50

50 but less than 60 4 2 .20 .10 20 10 20 1.00 100 Total (In a percentage histogram the vertical axis would be defined to show the percentage of observations per class) 8 Frequency Class DCOVA Histogram: Age Of Students 6 4 2 0 5

Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 15 25 35 45 55 More 2-44 Visualizing Numerical Data: The Polygon DCOVA 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. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-45 Visualizing Numerical Data: The Frequency Polygon DCOVA Class

Midpoint Frequency Class 15 25 35 45 55 3 6 5 4 2 Frequency Polygon: Age Of Students Frequency 10 but less than 20 20 but less than 30 30 but less than 40 40 but less than 50 50 but less than 60 (In a percentage polygon the vertical axis would be defined to show the percentage of observations per class) 7 6 5 4 3 2 1

0 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 5 15 25 35 45 55 65 Class Midpoints 2-46 Visualizing Numerical Data: The Ogive (Cumulative % Polygon) DCOVA 10 but less than 20 20 but less than 30 30 but less than 40 40 but less than 50 50 but less than 60 10 20 30 40 50 15 45

70 90 100 (In an ogive the percentage of the observations less than each lower class boundary are plotted versus the lower class boundaries. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall Ogive: Age Of Students Cumulative Percentage Class Lower % less class than lower boundary boundary 100 80 60 40 20 0 10 20 30 40 50

60 Lower Class Boundary 2-47 Visualizing Two Numerical Variables: The Scatter Plot DCOVA 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 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-48 Scatter Plot Example Cost per day 23 125 26 140 29 146 33 160

38 167 42 170 50 188 55 195 60 200 Cost per Day vs. Production Volume 250 200 Cost per Day Volume per day DCOVA 150 100 50 0 20 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall

30 40 50 60 70 Volume per Day 2-49 Visualizing Two Numerical Variables: The Time Series Plot DCOVA 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 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-50 Time Series Plot Example DCOVA Year

Number of Franchises Number of Franchises, 1996-2004 43 120 1997 54 100 1998 60 1999 73 2000 82 2001 95 2002 107 2003 99

2004 95 Number of Franchises 1996 80 60 40 20 0 1994 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 1996 1998 2000 2002 2004 2006 Year 2-51 Using Pivot Tables To Explore Multidimensional Data DCOVA

Can be used to discover possible patterns and relationships in multidimensional data. An Excel tool for creating tables that summarize data. Simple applications used to create summary or contingency tables Can also be used to change and / or add variables to a table All of the examples that follow can be created using Section EG2.3 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-52 Pivot Table Version of Contingency Table For Bond Data DCOVA First Six Data Points In The Bond Data Set Type Intermediate Government Intermediate Government

Intermediate Government Intermediate Government Intermediate Government Intermediate Government Assets Fees Return Expense Ratio 2008 3-Year Return 5-Year Return Risk 158.2 No 0.61 7.6 6.3 5.0 Average 420.6 No 0.61 8.9 6.7 5.3 Average 243.1 No

0.93 11.1 7.4 5.0 Above Average 24.7 No 0.49 7.3 6.5 5.4 Above Average 462.2 No 0.62 6.9 6.0 4.8 Average 497.7 No 0.27 11.4 7.7 5.9 Above Average

Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-53 Can Easily Convert To An Overall Percentages Table DCOVA Intermediate government funds are much more likely to charge a fee. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-54 Can Easily Add Variables To An Existing Table DCOVA Is the pattern of risk the same for all combinations of fund type and fee charge? Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-55 Can Easily Change The Statistic Displayed DCOVA This table computes the sum of a numerical variable (Assets) for each of the four groupings and divides by the overall sum to get the percentages displayed. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-56 Tables Can Compute & Display

Other Descriptive Statistics DCOVA This table computes and displays averages of 3-year return for each of the twelve groupings. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-57 Can Drill Down Into Any Cell In A Pivot Table DCOVA Double click in any cell to see a worksheet displaying the data that is used in that cell. Below is the worksheet created by drilling down in the short term corporate bond / fee yes cell. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-58 Principles of Excellent Graphs DCOVA 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. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-59 Graphical Errors: Chart Junk DCOVA Bad Presentation Minimum Wage 1960: $1.00 Good Presentation $ Minimum Wage 4 1970: $1.60 2 1980: $3.10 0 1990: $3.80 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 1960

1970 1980 1990 2-60 Graphical Errors: No Relative Basis Bad Presentation As received by students. Freq. 300 Good Presentation 20% 100 10% 0 0% SO JR SR As received by students. % 30%

200 FR DCOVA FR SO JR SR FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-61 Graphical Errors: Compressing the Vertical Axis DCOVA Bad Presentation 200 $ Quarterly Sales 50 100 25 0

0 Q1 Q2 Q3 Q4 Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall Good Presentation $ Quarterly Sales Q1 Q2 Q3 Q4 2-62 Graphical Errors: No Zero Point on the Vertical Axis DCOVA Bad Presentation $ Monthly Sales 45 42

39 36 42 39 J $ Monthly Sales 45 36 Good Presentations F M A M J 0 J F M A M

J Graphing the first six months of sales Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-63 Chapter Summary In this chapter, we have Organized categorical using a summary table or a contingency table. Organized numerical data using an ordered array, a frequency distribution, a relative frequency distribution, a percentage distribution, and a cumulative percentage distribution. Visualized categorical data using the bar chart, pie chart, and Pareto chart. Visualized numerical data using the stem-and-leaf display, histogram, percentage polygon, and ogive. Developed scatter plots and time series graphs. Looked at examples of the use of Pivot Tables in Excel for multidimensional data. Examined the dos and don'ts of graphically displaying data. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-64 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. Copyright 2011 Pearson Education, Inc. publishing as Prentice Hall 2-65