TABULAR REASONING LEARNING GUIDE

Transcription

1 TABULAR REASONING LEARNING GUIDE The materials used are developed from PEF files, Civil Service Documents in the Public Domain, and study guides developed by PEF. The State of New York Department of Civil Service has had no involvement in the creation of this study guide program. Any Civil Service materials used herein are in the public domain and included by design by PEF Membership Benefits. ALL RIGHTS RESERVED 2008 Kenneth Brynien, President Arlea Igoe, Secretary - Treasurer Trustees: Joe Fox, Chair Ken Brynien Arlea Igoe Pat Baker Tom Comanzo

2 Tabular Reasoning & Quantitative Analysis Creating, Understanding & Interpreting Information in Graphs This study guide is designed to help you build the knowledge and skills required to create, understand, and interpret data you will find in any graph so you can answer questions with varying levels of difficulty. The circle diagram represents five key skills for creating, understanding, and interpreting information in graphs. It is much like trivial pursuit --- you can start building any one of the five skills you want first, but you must have all five pieces to be successful. 1

3 Study Guide Overview: Creating, Understanding & Interpreting Information in Graphs What is a graph? A graph is visual representation of information. People typically use graphs to help demonstrate complex concepts or organize large sets of numerical data such as budgets, trends and inventory. Graphs make it easy for the reader to quickly locate and understand data without having to read through extensive quantities of written text. The purpose of this guide: This guide has been created to help you develop and refine skills that will enhance your ability to create and understand the diverse types of graphs you will be using in the work place. The strategies provided within this guide are proven to enhance the skills underlying the processes of creating, understanding, and interpreting information in graphs and have been tailored to meet the specific needs of PEF members preparing for the Civil Service Exams. Please note that this guide was not designed to be a practice test providing you samples of the types of questions or graphs you will see on the Civil Service Exams: Tabular Reasoning & Understanding and Interpreting Tabular Material/Qualitative Analysis. It was designed to help you build the knowledge and skills required to create, understand, and interpret data you will find in any graph so you can answer questions varying in level of difficulty. Rationale: In your work, you will be required to share and understand diverse types of data across various levels in your organization. Some data such as policies and memos will be best explained using prose; while other information such as budgets, economic trends, consumer trends and inventory will be organized into various graphs to support easy dissemination and comprehension. It is important that you understand how to read various types of graphs, how to select and build the appropriate graph to support the information you are summarizing, and how to interpret information provided in different graphs. Components of this guide: This study guide consists of five modules including Types of Graphs, Key Elements of Graphs, Creating Graphs, Summarizing and Comparing Information in Graphs, and Drawing Conclusions from Graphs. It is recommended that you begin with the first module and work your way through the remaining four modules. At the end of the study guide, you will find three appendices to support your studies: Hints for Tables & Graphs, Mathematical Vocabulary & Concepts and Mathematical Operations. If you find that you need additional practice completing mathematical operations or solving mathematical problems a list of additional resources has been provided at the conclusion of the study guide. Next, you will find a brief explanation of the five modules in this study guide. Following the brief explanations, you will find the expanded modules containing the learning material, examples, explanations, and practice questions. 2

4 A. Types of Graphs Summary This is the first module included in the Tabular Reasoning & Qualitative Analysis study guide. It provides an overview of the five types of graphs that you will be asked to create, read, interpret, and draw conclusions from in your work and on the Civil Service Exams. This will include tables, line graphs, area graphs, bar graphs, and pie charts. The purpose of this module is for you to be able to recognize the different types of graphs and identify the type of information that is typically displayed in each type of graph. This will allow you to develop the skills needed to read, understand, create, and fill-in graphs. B. Key Elements of Graphs Summary This is the second module included in the Tabular Reasoning & Quantitative Analysis study guide. This section will outline the various components of each type of graph you will manipulate in your work and during the Civil Service Exams. The purpose of this module is for you to be able to identify the various elements of each type of graph thus easing your ability to understand, interpret, create, and fill-in partially completed graphs. Figure 1.1 is a sample of the content contained in this section. Figure 1.1: Sample Graph with Elements Labeled (Smith & Sons Profits ) Graph Title Y-Axis Label Smith & Sons Profits ( ) Y-Axis Profits (thousands) Years X-Axis X-Axis Label 3

5 C. Creating Graphs Summary This is the third module included in the Tabular Reasoning & Quantitative Analysis study guide. The module explains how three of the five types of graphs presented in this study guide are created: tables, line graphs, and bar graphs. By learning how to create these types of graphs, you will build the skills required to read and interpret them in order to answer questions on the Civil Service Exam and in the work place. In this module, you will find three examples. Each example provides data in a paragraph. Then it provides a detailed explanation of how to select the correct graph to represent the data, extract the important information from the paragraph, and create the graph. Below, you will see an example of the paragraphs found in this module. Example 1.1: Sample Paragraph The Calvary Group has three offices: San Jose, CA, St. Petersburg, FL, and New York, NY. Two days before the VP of Marketing at Calvary Group is to present to the senior staff, they requested to see the comparison of airfare expenditures for 2006 within the Marketing Department per office, in order to determine where their travel money was being spent in So the VP requested data that aggregated the data per office for The data she received stated the following: San Jose, CA had 5 executives and 22 sales representatives from the marketing department travel during There were 55 trips via plane costing $75, and 28,547 miles traveled via car costing $12, The St. Petersburg office had 2 executives and 35 sales representatives take 22 trips via plane costing $18,700 and travel 15,798 miles via car costing $7, The New York office had 4 executives and 75 representatives travel during Fifty-six trips were via plane costing $56,600, and the employees traveled 56,470 miles via car costing $12, D. Summarizing and Comparing Information Summary The fourth module offers practice in reviewing variables in a graph, organizing them in meaningful ways and comparing and contrasting the information to observe trends. The examples will show headings, graphs with variables, brief explanations and questions. A sample is provided below. 4

6 Example 1.2: Sample Comparative Graph Internet use at Rosewood Secondary School, by sex, Number of Students Boys Girls One disadvantage of vertical bar graphs, however, is that they lack space for text labeling at the foot of each bar. When category labels in the graph are too long, you might find a horizontal bar graph better for displaying information. Data comparisons can be made by yearly analysis, trends over various periods (i.e., vs ) and trends by gender. Further analysis of specific numbers of the population by ages could be obtained which could provide further data comparisons and summarizations. E. Drawing Conclusions Summary This section is provided to help you think about the implications of data presented in a particular context. While some of the conclusions are easily drawn from the graphs, many conclusions cannot be made because of the sample size of information or lack of controlled variables. This example of a double horizontal bar graph is created based on a survey of an equal number of boys and girls at a high school. They were asked to pick their preferred snack from the list below. Popcorn Pretzels Candy Chips Cookies Vegetable Chocolate bar Ice cream Crackers Fruit 5

7 The graph summarizes their responses. Preferred snack choices of students at St. John's high school Vegetables Pretzels Popcorn Ice Cream Fruit Crackers Boys Girls Cookies Chocolate Bars Chips Candy Number of Students Meaningful conclusions that could be drawn from this graph are: Girls least preferred snack was vegetables while fruit was the most preferred. A substantial number of boys prefer chips compared to girls. The same number of boys and girls preferred popcorn as their snack food choice. 6

8 Section A Types of Graphs Purpose: The purpose of this module is to provide an overview of the types of graphs you will be asked to read, interpret, analyze, and draw conclusions from during the following Civil Service Exams: Tabular Reasoning & Understanding and Interpreting Tabular Material II/Qualitative Analysis. By completing this module: 1. You will recognize the different types of graphs. 2. You will be able to identify the type of information that is typically displayed in tables, line graphs, area graphs, bar graphs, and pie charts. Rationale: It is important that you are able to identify the various types of graphs that you must interact with during the Civil Service Exams and at work so that you can readily understand them. Not only must you be able to identify the graphs, but you must also understand what types of content are contained in each type of graph. This knowledge will increase your ability to understand graphs and read and interpret the data contained within them. Explanation: The module provides an explanation of the following types of graphs: tables, line graphs, area graphs, bar graphs, and pie charts. In addition, it provides the type of data that each graph would contain and provides you a sample of the different graphs. 7

9 1. Tables: Tables are used to organize information that is best presented using rows and columns to make it easier for the reader to understand. Types of data typically represented using tables include statistics, salaries, budgets, census data, inventory data, work schedules, and business expenses. Figures 2.1 and 2.2 are example of tables. Figure 2.1 shows a summary budget over four fiscal years, and Figure 2.2 shows an end of the year report for employee vacation days. Figure 2.1: Sample Table (Summary Budget) Summary Budget Over Four Fiscal Years FY2003 FY2004 FY2005 FY2006 Salary (total) 1,500, ,650, ,898, ,230, Executives (2) 150, , , , Managers (2) 75, , , , Shift Supervisors (3) 90, , , , Employees (75) 1,185, ,304, ,499, ,762, Benefits (82) 203, , , , Travel 10, , , , Per Diem Supplies 25, , , , Miscellaneous 20, , , , Figure 2.2 Sample Table (End of the Year Report: Employee Vacation Days) End of the Year Report: Employee Vacation Days Days Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Employees Elizabeth Fitzgerald Samuel Halloford Roger Milliano Days Left 2. Line Graphs: Line graphs are mostly used to visually represent tabular data. They are often used to show changes over time or trends. They have an x-axis (horizontal) and a y-axis (vertical). The x- axis has numerical values for each time period you want to use and the y-axis has numbers for what is being measured. People use line graphs when it is important that the reader can see the change between one point in time and another such as revenue for 2005 and revenue for At significant times, such as weekly, monthly, or yearly, the data is put on the graph to create dots. Then a line is drawn to connect the dots. Types of data typically represented using line graphs include change in revenue over time, change in census data over time, change in business expenses over time, and change in cost over time. Figure 2.3 shows an example of a line graph displaying the cash flow trends over FY

10 Figure 2.3: Sample Line Graph (FY 2006 Cash Flow Trends) FY 2006 Cash Flow Trends 500 Cash Flow (thousands) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months 3. Area Graphs: Area graphs are line graphs with the area below the line shaded in. Like line graphs, they are used to show trends over time; however their appearance focuses the reader on the quantities verses the actual trends. Just like line graphs, the types of data typically represented using area graphs include change in revenue over time, change in census data over time, change in business expenses over time, and change in cost over time. Figure 2.4 shows an area graph displaying the minimum wage trends from Figure 2.4: Sample Area Graph (Federal Minimum Wage Trends) Federal Minimum Wage Trends Minimum Wage Rate Years 4. Bar Graphs: Bar graphs are used to show comparisons among different categories using an x- axis and a y-axis. They can be horizontal or vertical; however despite the layout, one axis always shows the specific categories being compared while the other axis is always used to define the discrete value being measured. Types of data typically represented using bar graphs include expenditures or budgets for various departments in an organization, quantities of product being produced in various regions, amounts of revenue for several years, the number of employees per 9

11 year, data showing consumer preferences per product, and census data showing average income in various locations. Figures 2.5 and 2.6 are examples of bar graphs. Figure 2.5 displays the number of employees per region in a vertical bar graph, and figure 2.6 displays the same data in a horizontal bar graph. Figure 2.5: Sample Bar Graph (vertical) Figure 2.6: Sample Bar Graph (horizontal) Employees per Region Employees per Region Number of Employees (thousands) R e g io n Region E Region D Region C Region B Region A Region A Region B Region C Region Region D Region E Number of Employees (thousands) 5. Pie Charts: Pie charts are used to show proportions of a whole of something measured at one point in time. Each slice of the pie represents the proportion of the specific category to the entire whole. Types of data typically represented in pie charts include percentages of consumers buying various items and the percentages of a budget spent on developing various components of a product. Figure 2.7 is a sample pie chart which shows the New York Ethnic Diversity as reported by the Census Bureau in Figure 2.7: Sample Pie Chart New York Ethnic Diversity (2000 Census) 2.74% 6.37% 0.04% 5.65% 0.39% 14.77% 70.03% White Black AI or AN Asian NH or OPI Other Mixed 10

12 Section B Key Elements of Graphs Purpose: The purpose of this module is to outline the key elements of the types of graphs you will be asked to read, interpret, analyze, and draw conclusions from during the following Civil Service Exams: Tabular Reasoning and Understanding & Interpreting Tabular Materials. By completing this module you will be able to: 1. Define the elements of each type of graph. 2. Label the elements of each type of graph. Rationale: It is important that you are able to identify the elements of tables, line graphs, area graphs, bar graphs, and pie charts. By knowing the elements of the various graphs, you will be able to complete incomplete graphs, create new graphs using provided data, and understand the data in the graphs that are presented to you on the Civil Service Exams and in the work place. Explanation: In this module you will find examples of each of the types of graphs covered in this study guide. Each graph will be labeled to identify key elements of that graph, and at the conclusion of the module you will be required to label various graphs using the data you are provided. 11

13 1. Tables: As you learned in the previous module, tables are used to represent data that is best presented using rows and columns such as statistics, salaries, budgets, census data, work schedules, etcetera. 1 A table consists of a title for the table, a series of horizontal rows containing categories (such as worker s names, organizational departments, or products), and a series of vertical columns that typically represent time frames (months, days, or years). In addition, each column and row has a title. Without the appropriate elements, a table can be quite difficult to understand. Without a title, the content of the table is unknown, and without clearly defined rows and columns it can be difficult for the reader to know which data goes with which category. Let s take a look at an example. Figure 3.1 is a graphical representation of a business budget spanning four fiscal years. The title of the table is Summary Budget over Four Fiscal Years. The horizontal rows are different areas of the budget such as salaries, benefits, travel, and supplies while the vertical columns are the four years being reported. Once the labels for the graph, rows, and columns are in place, inputting the data becomes relatively easy. Figure 3.1: Sample Table (Summary Budget Over Four Fiscal Year) Table s Title Series of Horizontal Rows with Row Labels Summary Budget Over Four Fiscal Years FY2003 FY2004 FY2005 FY2006 Salary (total) 1,500, ,650, ,898, ,230, Executives (2) 150, , , , Managers (2) 75, , , , Shift Supervisors (3) 90, , , , Employees (75) 1,185, ,304, ,499, ,762, Benefits (80) 203, , , , Travel 10, , , , Per Diem Supplies 25, , , , Miscellaneous 20, , , , Series of Vertical Columns with Column Labels 2. Line Graphs: As you ve already learned, line graphs are used to represent changes over time or trends. They are created by using an x-axis (horizontal) and a y-axis (vertical) versus the rows and columns used in tables. The x-axis is labeled using the times you want to display such as months, weeks, days, or years. The y-axis is labeled using the increments you are measuring such as money, size or any other type of number. Line graphs are used instead of tables when you want to emphasize the size of the change over time. Where a table can display several elements, a line graph is best used to display one to three elements only. This is because the more trends you want to show, the more cluttered the line graph becomes thus making it difficult to read. 1 Definition is from Wikipedia found on 10/26/2006 at 12

14 As with a table, a line graph must contain certain elements in order for the user to be able to understand the graph. A line graph consists of a graph title stating the content of the graph, an x- axis with labels for the time frames you re measuring, a y-axis with labels for the measurement increments, and x-axis and y-axis titles. In addition, a line graph contains dots, or plots, where you plot the information, and a line drawn to connect the dots. A line graph can be very difficult to understand if any of the elements are missing. Let s take a close look at Figure 3.2. The graph title is Summary Budget of Salaries over Four Fiscal Years. It was created using the data from the first row in Figure 3.1 to emphasize the increasing trend. The x-axis shows the same fiscal years used in Figure 3.1 (2003, 2004, 2005, and 2006). The y-axis shows the cost in millions, so 1.0 equals one million (1,000,000), 1.2 equals 1,200,000, and so on. The salaries are plotted at each year using a dot, and then the dots are connected with a line. Figure 3.2: Sample Line Graph (Summary Budget of Salaries over Four Fiscal Years) Y-Axis Title Y-Axis with Labels for the measurement increments Cost (millions) Summary Budget of Salaries over Four Fiscal Years FY2003 FY2004 FY2005 FY2006 Fiscal Years Line Graph s Title Dot or Plot Line Connecting Each Plot X-Axis with labels for each time frame being measured X-Axis Title Area Graphs: You already know that area graphs are very similar to line graphs; both types of graphs are used to display trends over time and they contain all the same elements. The only difference is that an area graph is used to focus the reader on the quantity versus the actual trends. This is done by shading in the area below the line. Figure 3.3 displays the same data shown in Figure 3.2 and contains the same elements found in Figure 3.2 including a graph title stating the content of the graph, an x-axis with labels for the time frames you re measuring, and a y-axis with labels for the measurement increments, x-axis and y-axis titles, dots or plots, where you plot the information, and a line drawn to connect the dots. The only difference is that the area below the line is shaded in creating a shaded area to emphasize the quantity at each point on the x-axis. Take a look at Figure 3.3. The graph title, Summary Budget of Salaries over Four Fiscal Years, tells you that it contains the same data as Figure 3.2. The x-axis shows the same fiscal years used in Figure 3.2 (2003, 2004, 2005, and 2006). The y-axis shows the cost in millions, so 1.0 equals 13

15 one million (1,000,000), 1.2 equals 1,200,000, and so on. The salaries are plotted at each year using a dot, and then the dots are connected with a line. The only difference is that in Figure 3.3 the area below the line is shaded in. Why? The area graph is meant to focus the reader on the quantity versus the actual trends. Figure 3.3: Sample Area Graph (Summary Budget of Salaries over Four Fiscal Years) Y-Axis Title Summary Budget of Salaries over Four Fiscal Years Area Graph s Title 2.00 Y-Axis Cost (millions) Dot or Plot 1.00 FY2003 FY2004 FY2005 FY2006 Fiscal Years Line Connecting Each Plot Numeric Labels for X and Y Axes Shaded in Area X-Axis X-Axis Title Bar Graphs: During the introduction section of the study guide, you learned that bar graphs are used to show comparisons among different categories of information. Like line graphs and area graphs, they contain an x-axis and a y-axis. However the x-axis and y-axis are not restricted to time frames and numeric values like they are in line graphs and area graphs. In bar graphs, one axis typically contains a numeric value that is being measured, while the other axis can contain a variety of types of information. Some examples are factory names, employee names, departmental names, types of products, years, and geographic locations. As you observed in Figures 2.5 and 2.6, the same data can be represented using horizontal bar graphs or vertical bar graphs. It doesn t matter which type of bar graph you use as long as the axes have titles and labels that make the graph readable. Bar graphs, just like any other type of graph, must contain certain elements in order for the reader to be able to understand and interpret the information contained in them. Just like line graphs and area graphs, they have a graph title stating the content of the graph, an x-axis with labels, and a y-axis with labels. In addition, many bar graphs come with legends to help you understand the graph. Figure 3.4 displays the number of employees at each factory within an organization. The legend at the right of the graph provides additional information to help the 14

16 reader interpret the graph; in this particular example it provides the exact number of employees per factory. Let s look at Figure 3.4. The graph title is Employees per Region. The x-axis shows the factory locations and is labeled using each factory s name. The y-axis shows the number of employees and is labeled using numbers in the thousands so 25 equals 25,000, 50 equals 50,000, and so on. In addition, there is a legend which helps the reader interpret the graph. Figure 3.4: Sample Bar Graph (Employees per Region) Y-Axis Title Employees per Region Bar Graph s Title Y-Axis with labels showing the measurement increments Number of Employees (thousands) Legend Legend Region A 300, 000 Region B 200,000 Region C 15, 000 Region D 20,000 Region E 45, 000 Region A Region B Region C Region Region D Region E X-Axis Title X-Axis with labels for each region Pie Charts: Tables, line graphs, area graphs, and bar graphs can represent data in numeric values such as hundreds, thousands, or millions. However, pie charts are only used to compare data in percentages. In addition, pie charts can only display data from one point in time such as 2006 or July of They cannot display data over a span of time like all the other graphs discussed. Pie charts received their name because they look like a pie cut into various size slices. Pie charts are rather simple. The only elements they contain is a graph title to tell what the graph is about, pie slice labels that tell the percentage being shown, and a legend to help the reader understand what categories the various shades or colors of the pie slices represent. Let s take a look at Figure 3.5. The graph title is Employees per Region, and it shows the same data from Figure 3.4. However, instead of showing exact values as in Figure 3.4, Figure

17 shows the values as percentages of the total number of employees. The legend tells you what categories the various colors represent. Figure 3.5: Sample Pie Chart (Employees per Region) Pie Chart s Title Pie Slice Labels Employees per Region 7.76% 3.45% 2.59% 51.72% 34.48% Region A Region B Region C Region D Region E Legend 16

18 Section C Creating Graphs Purpose: The purpose of this module is to build key skills so that you will be able to complete partially completed tables and graphs and build tables and graphs using data presented in a narrative or paragraph format. By completing this module you will be able to:: 1. Complete partially completed tables and graphs from data presented in a narrative format. 2. Create tables and graphs from data presented in a narrative format. Rationale: On the Civil Service Exams you might be asked to interpret data presented in paragraph form. Having the skills to represent that data in tables and charts will help you organize all the information presented in the paragraph. Once you have been able to organize all the information given, understanding and interpreting the information becomes easier. Explanation: This module will present information in paragraph form and then organize the information into tables, line graphs, or bar graphs. These are the three types of graphs that you will most frequently be asked to complete on the Civil Service Exams and in the workplace and they are easy ways to organize information. 17

19 1. Tables: Calvary Group Example I The Vice President of Marketing at Calvary Group is reviewing travel expenditures for the marketing department over the last three years in order to prepare a presentation on the expenditures within the department for the senior staff meeting next week. The marketing department spent $200,000 on airfare, $375,000 on employee lodging and meals, $80,000 on mileage, and $58,000 on car rentals in In 2005, they spent $220,000 on airfare, $412,500 on employee lodging and meals, $72,000 on car rentals, and $46,400 on mileage. Travel expenditures for 2006 totaled $793,000. It included $154,000 on airfare, $495,000 on employee lodging and meals, $57,600 on car rentals, and $86,400 on mileage. The question is: What type of graph should be used to help the VP of Marketing at Calvary Group display all these data so the senior staff can easily view them? The introduction section of this study guide explained what the different graphs are used for. Tables organize information best displayed using rows and columns. Line graphs and area graphs are used to show trends, bar graphs show comparisons among different categories in one point of time and pie charts are used to display data in percentages at one point in time. If we reflect on the information above in Calvary Group Example I, we see that there is data for three different points of time. Since pie charts can only be used to display data at one point in time, this choice is out. Line graphs and area graphs are used to show trends over time. The VP doesn t want to display trends (she just wants to display all the data), so line graphs and area graphs are not the best choices either. Bar graphs compare categories, but we re not comparing categories in this example. Our goal is to simply display all the data. To display all the data in Calvary Group Example I, the VP should use a table, because this data is best displayed using columns and rows. Using Figure 3.1 as an example, we see that the columns are the years, and the rows are the different categories. So, our table for Calvary Group Example I would look the same, but with different years in the columns across the top and different categories in the rows down the side. In Calvary Group Example I, the three years are 2004, 2005, and 2006 and the categories include airfare, employee lodging & meals, car rentals, and mileage. See Figure 4.1 to see how the table would be set-up. Calvary Group Budget ( ) is the title; 2004, 2005, and 2006 are the column labels across the top; and airfare, employee lodging & meals, car rentals, and mileage are the labels of the rows. Figure 4.1: Table for Calvary Group Example I Calvary Group Budget ( ) Airfare Employee Lodging & Meals Car Rentals Mileage 18

20 After the table is set-up, the next task is to input all the data given in the paragraph from the Calvary Group Example. To do this, simply put all the information for 2004 in the correct rows, all the information for 2005 in the correct rows, and so on. The table in Figure 4.2 begins to input the data. It is recommended that you complete the table using the data provided in Calvary Group Example I. Correct answers are provided in the Answer Key found at the end of the guide. Figure 4.2: Partially Completed Table for Calvary Group Example I Summary Budget over Three Years Airfare 200, Employee Lodging & Meals 375, Car Rentals 58, Mileage 80, Line Graphs: Calvary Group Example II The Vice President of Marketing at Calvary Group is reviewing travel expenditures again for the marketing department over the last three years in order to prepare a presentation on the expenditures within the department for the senior staff meeting next week. Not only does the senior staff want to see all the data; they have requested to see the trends in airfare expenditures and car rentals. The marketing department spent $200,000 on airfare, $375,000 on employee lodging and meals, $80,000 on mileage, and $58,000 on car rentals in In 2005, they spent $220,000 on airfare, $412,500 on employee lodging and meals, $72,000 on car rentals, and $46,400 on mileage. Travel expenditures for 2006 totaled $793,000. It included $154,000 on airfare, $495,000 on employee lodging and meals, $57,600 on car rentals, and $86,400 on mileage. The question is: What type of graph should be used to help the VP of Marketing at Calvary Group display the trends in these data so the senior staff can easily view them? The introduction section of this study guide explained what the different graphs are used for. Tables organize information best displayed using rows and columns. Line graphs and area graphs are used to show trends, bar graphs show comparisons among different categories in one point of time and pie charts are used to display data in percentages at one point in time. If we look carefully at the question above, we see that the VP of Marketing has to show trends. We know that tables display data best represented in rows and columns and there is nothing to say that they are used to display trends, so tables are out. A pie chart is used to show percentages, but the question doesn t ask for percentages, so a pie chart is out. Bar graphs show comparisons among different categories, but we re not asked to compare, so bar graphs are not the best choice either. 19

21 The VP has been asked to show trends. Line graphs and area graphs are the best option. Which one do we choose? Let s reflect on what we learned in the Introduction section of this study guide: Line graphs and area graphs show trends, but area graphs are used to focus the reader on the quantities versus the actual trends. Since we want to focus on the trends and not the actual quantities, we would use a line graph, not an area graph. A great deal of information is provided in the Calvary Group Example II above, but we don t need to use all of it. How do we select which information is relevant? We go back to the paragraph and find: Not only does the senior staff want to see all the data; they have requested to see the trends in airfare expenditures and car rentals. This means that the only data we have to find in the paragraph is the data for airfare and car rentals for each of the years (2004, 2005, and 2006). The paragraph is restated below highlighting the needed information. The Vice President of Marketing at Calvary Group is reviewing travel expenditures again for the marketing department over the last three years in order to prepare a presentation on the expenditures within the department for the senior staff meeting next week. Not only does the senior staff want to see all the data; they have requested to see the trends in airfare expenditures and car rentals. The marketing department spent $200,000 on airfare, $375,000 on employee lodging and meals, $80,000 on mileage, and $58,000 on car rentals in In 2005, they spent $220,000 on airfare, $412,500 on employee lodging and meals, $72,000 on car rentals, and $46,400 on mileage. Travel expenditures for 2006 totaled $793,000. It included $154,000 on airfare, $495,000 on employee lodging and meals, $57,600 on car rentals, and $86,400 on mileage. How do we build the line graph? We have to show two trends, so we would make two separate line graphs. We need include all the elements of a line graph from Figure 3.2 including a line graph title, and x-axis and y-axis with titles and labels, dot (plots), and a line connecting each plot. Then, using Figure 3.2 as an example, we can see that the years go on the x-axis across the bottom and the amounts go on the y-axis up the side with the smallest amount at the bottom. Let s create the line graph for airfare first. In Calvary Group Example II, there are three years (2004, 2005, and 2006) which will be our three years for the x-axis. The lowest amount for airfare in the example is $154,000 and the highest amount is $220,000. These will be our lowest and highest amounts for the y-axis. We re talking about thousands, so we would use $154 and $220 as labels for the y-axis as long as we make sure that are axis title says thousands. Look at Figure 4.3 to see how the line graph would be set up. 20

22 Figure 4.3: Line Graph Airfare Expenditures in Calvary Group Example II Airfare Expenditures Expenditure (thousands) Years After the line graph is set-up, the next task is to input the data from the example. To do this, simply put a dot for each year at the correct value. For 2004, the airfare expenditures were $200,000 (200 on the graph); for 2005, the airfare expenditures were $220,000 (220 on the graph); and for 2006, the airfare expenditures were $154,000 (154 on the graph). Once the dots (plots) have been made, simply draw a line between the dots to show the trends. See Figure 4.4 to see how this is done. Figure 4.4: Complete Line Graph Airfare Expenditures in Calvary Group Example II Airfare Expenditures Expenditure (thousands) Years 21

23 Remember, that the example stated, Not only does the senior staff want to see all the data; they have requested to see the trends in airfare expenditures and car rentals. This means we still have to create a line chart for the expenditures for car rentals. Figure 4.5 sets up the graph for you. It is recommended that you plot the chart and draw the line to create the line graph. Correct answers are provided in the Answer Key found at the end of the guide. Figure 4.5: Partially Completed Line Graph Car Rental Expenditures in Calvary Group Example II Car Rental Expenditures Expenditure (thousands) Years 2. Bar Graphs: Calvary Group Example III The Calvary Group has three offices: San Jose, CA, St. Petersburg, FL, and New York, NY. Two days before the VP of Marketing at Calvary Group is to present to the senior staff, they requested to see the comparison of airfare expenditures for 2006 within the Marketing Department per office, in order to determine where their travel money was being spent in So the VP requested information that aggregated the data per office for The data she received stated the following: San Jose, CA had 5 executives and 22 sales representatives from the marketing department travel during There were 55 trips via plane costing $75, and 28,547 miles traveled via car costing $12, The St. Petersburg office had 2 executives and 35 sales representatives take 22 trips via plane costing $18,700 and travel 15,798 miles via car costing $7, The New York office had 4 executives and 75 representatives travel during Fifty-six trips were via plane costing $56,600, and the employees traveled 56,470 miles via car costing $12, The question is: What type of graph should be used to help the VP of Marketing at Calvary Group display a comparison in these data so the senior staff can easily view them? The introduction section of this study guide explained what the different graphs are used for. Tables organize information best displayed using rows and columns. Line graphs and area graphs are used to show trends, while bar graphs show comparisons among 22

24 different categories in one point of time and pie charts are used to display data in percentages at one point in time. Reflecting on the information provide in Calvary Group Example III, we see that the VP has to show a comparison between the airfare from the three office locations. We know that tables used to show data using rows and columns, but it doesn t say anything about using them to show comparisons. Tables are not the best choice. Line graphs and area graphs are used to show trends; we want to show a comparison, so line graphs and area graphs are out. Pie charts can only show percentages, so that s not an option because we re using exact quantities. The VP has been asked to show comparisons, so bar graphs are the best choice. Remember, it doesn t matter if we use horizontal or vertical bar graphs as long as they are labeled. Calvary Group Example III contains many numeric values, but not all of them are relevant to the request the senior staff made: they requested to see the comparison of airfare expenditures for 2006 within the Marketing Department per office. This means that the only information we have to find in the example is the data regarding the airfare for The paragraph is restated below highlighting the needed information. San Jose, CA had 5 executives and 22 sales representatives from the marketing department travel during There were 55 trips via plane costing $75, and 28,547 miles traveled via car costing $12, The St. Petersburg office had 2 executives and 35 sales representatives take 22 trips via plane costing $18,700 and travel 15,798 miles via car costing $7, The New York office had 4 executives and 75 representatives travel during Fifty-six trips were via plane costing $56,600, and the employees traveled 56,470 miles via car costing $12, Let s set up the bar graph so we can input the data. How do we do this? We use the elements shown in Figure 3.4 including a graph title, a y-axis with labels showing the measurement increments, an x-axis with labels for each category, x-axis and y-axis titles, and a legend. Then, using Figure 3.4 as an example, we can see that the measurement increments go on the y-axis up the side of the graph and the categories go across the bottom on the x-axis. Note that if you choose you can switch the x-axis and y-axis. In Calvary Group Example III, there are three offices for which we must show the airfare expenditures: San Jose, St. Petersburg, and New York. These office names will be our category titles for the x-axis. The lowest amount for airfare is $18,700 and the highest amount for airfare is $75, We re talking about thousands, so we would use $18 and $76 as labels for the y-axis as long as we make sure that the axis title says thousands. Look at Figure 4.6 to see how the graph would be set up. (Figure 4.7 is the same information graphed using a horizontal graph.) 23

25 Figure 4.6: Vertical Bar Graph Airfare Expenditures by Office Location at Calvary Group Figure 4.7: Horizontal Bar Graph Airfare Expenditures by Office Location at Calvary Group Airfare Expenditures for 2006 Expenditures (thousands) San Jose St. Petersburg New York Calvary Group Office Location Calvary Group Office Location Airfare Expenditures for 2006 New York St. Petersburg San Jose Expenditures (thousands) After the graph is set up, the next task is to input the data from the example. To do this, draw a rectangle from the spot on the x-axis (location) where the location of the office is to the amount on the y-axis (the expenditure) that represents amount stated in Calvary Group Example III. The example states, for 2006, San Jose, CA had 5 executives and 22 sales representatives from the marketing department travel during There were 55 trips via plane costing $75,801. The St. Petersburg office had 2 executives and 35 sales representatives take 22 trips via plane costing $18,700. The New York office had 4 executives and 75 representatives travel during Fifty-six trips were via plane costing $56,600 See Figure 4.8 to see how this is done in the vertical bar graph. Figure 4.9 is a replication of Figure 4.7. It is recommended that you complete the bar graph. Correct answers are provided in the Answer Key found at the end of the guide. Figure 4.8: Vertical Bar Graph Airfare Expenditures by Office Location at Calvary Group Figure 4.9: Horizontal Bar Graph Airfare Expenditures by Office Location at Calvary Group Airfare Expenditures for 2006 Expenditures (thousands) Airfare Expenditures for 2006 San Jose St. Petersburg New York Calvary Group Office Location Calvary Group Office Location New York St. Petersburg San Jose Expenditures (thousands) 24

26 Section D Summarizing and Comparing Information Purpose: This module represents the most widely used graphs and questions found on the Civil Service exam. Contained in this section are various charts and graphs with questions that require you to: 1. Read headings and X, Y axis variables clearly 2. Understand how measurements are related 3. Observe relationships and key data points 4. Conduct arithmetic calculations as required 5. Select correct answer from multiple choice lists Rationale: This module will prepare you to become a keen observer of materials presented and to understand the relationships between the data that provides information useful to understanding the intent of the graph. This practice will help you to become familiar with the types of problems on the exam, and also will help you to understand the mental reasoning needed in making accurate interpretations of the material and graphs. Explanation: The module starts out with a "decision tree" consisting of 3 stages that will help guide you in reviewing each chart / graph. Glance through it to understand the flow and critical steps in the decisions you will make. The remainder of this section will show examples of charts / graphs with questions and explanations to help you understand the varied approaches the exam may include. The answer key is provided at the end of the guide. 25

27 DECISION TREE The following mental decision process map is created to help guide your mental thought process in an analytic manner. While answers to questions may not require this process, it is created as a due diligence thought sequence which could prevent errors from erroneous assumptions and/or trick questions. What is the purpose of the graph? What headings are presented? What footnotes are used and what is their meaning? What subheadings are presented? What groupings or classifications are made on the x and y axis?: -duplication -natural groupings What data sample size is depicted? Practice Questions Use the charts displayed to answer the questions located after the graphs. Questions 1.0 Chart 1-1 Work Life Top 5 Issues Related Web Hits January 2006 through December # of Hits Specific Issues Childcare Budget/Finance Pre-Tax Savings Health Resources Mental Health 26

28 Chart 1-2 Note carefully that the questions below are associated with both Charts 1-1 and 1.2. If you need some help with the questions, learning notes are provided after the last question in the section. Q1. What are the lowest 3 issues employees have sought information on the web about? 1. Mental health, health resources, childcare 2. Budget, pre-tax savings, mental health 3. Health resources, mental health, pre-tax savings 4. Childcare centers, flex spending, NYS ride Q2. About how many hits are there for Childcare and Budget issues? Q3. What is the approximate range between the lowest category of web hits to the highest number of web hits?

29 Q4. What broad category appears to be the most sought after in web pages? 1. Retirement 2. Health 3. Childcare 4. Financial planning Learning Notes (1.0/1.1) 1. Chart Headings Study the headings of the charts and the x, y axis to understand the purpose of the chart. NOTE: Chart 1: Displays top 5 issues (web hits) over the period of January-December 2006 Chart 2: Displays volume of work life services main web page hits, January-December Analyze Questions Questions may be related to either chart so be conscious of what variables the question is addressing. Q1 Issue focused Chart 1 (Note: carefully select lowest categories) Q2 Work life Chart 1 (We are looking for the combined number of hits for two specific issues) Q3 Work life Chart 2 (Note: the range is the number of units between the highest and lowest values.) i.e =? Q4 Work life Chart 2 (Note: Total the categories by category area) i.e. Childcare area = childcare center list + childcare center = about about 4000 = about This is the largest number of the categories listed. 28

30 Questions 2.0 Chart 2-1 Unemployment Rate Learning Note: You may want to use the straight edge of a piece of paper to approximate values on the vertical scale. This may improve your visual accessing of approximate values. Note carefully that the questions below are associated with Chart 2-1. Q1. What is the approximate unemployment rate increase at the onset of the most recent recession in March 2001 to January 2002? % - 5.8% % - 9.5% % % 4. Data insufficient to answer Q2. What is the approximate cumulative percentage of increases in unemployment rates based on recessions in 1974/1975 and 1981/1982? 1. 8% 3. 4% 2. 5% 4. 0% Q3. What is the difference in percentage between the highest unemployment rate and the lowest employment rate in the given time period? 1. 10% 3. 7% 2. 4% 4. 0% Q4. What period had the lowest overall change in unemployment rates?

31 Chart 3.0 Preferred Snack Choices Preferred snack choices of students at St. John's high school Vegetables Pretzels Popcorn Ice Cream Fruit Crackers Boys Girls Cookies Chocolate Bars Chips Candy Number of Students Questions 3.0 Q1. What is the approximate percentage difference between the number of boys and girls in the study? 1. 0% % 2. 15% 4. 50% Q2. In a percent, how many more girls preferred fruit compared to boys? 1. 73% 3. 0% 2. 17% % Q3. What ratio of category preferences did the boys exceed the girls in? 1. 4:5 3. 1:1 2. 5:4 4. 5:5 Q4. Approximately how many students had snacks at the school? Summary This section, Section D -Summarizing and Comparing Information, contained examples of various charts that you will find on the Tabular Reasoning examination. The purpose of this section is to enable you to find the important categories represented and then to locate the values or measures related to the categories. To enhance your learning and review, you may find using the decision tree as a reference when reading the graphs helpful. The Answer Key is at the end of this guide for your review. 30

32 Section E Drawing Conclusions Purpose: This module is composed of several tables that have been modified from NYS reports. Please note that data may be missing in the charts or there may be duplication of categories. You can calculate information to make the charts complete by analyzing variables in both the vertical and horizontal columns. Also notice that often multiple charts are presented in reports that change one or two variables. Make sure to answer the questions from the appropriate data. Rationale: While this module may appear more complex with multiple tables and graphs, it requires the same mental process as the previous module. By first understanding the intent of the table / chart / graph you can proceed with your analysis of the questions. Remember that the graphs in the sections are reconfigured NYS tables. Explanation: The three tables may lead to multiple correct answers to the questions at first glance. So, be careful about jumping to immediate conclusions as you select your response. The correct answers are located at the end of the guide. 31

33 Chart 1.0 Agency Accident Reports 2006 YTD Total July August September October November December Bending Blood to Blood Exposure Blood to Blood/Consumer Assault Consumer Assault Consumer Lifting/Transfer Consumer Other Consumer SCIP Environment Exposure Faulty Equipment Motor Vehicle Accident Object Lifting Other Providing Assistance to Consumer Reaching Repetitive Movement Slippings Sports Injury Staff Action Stress Trips Period Totals:

34 Questions 1.0 Q1. What are the top 3 issues during the summer months (July and August)? 1. Consumer assault, consumer assistance, staff action 2. Trips, slippings, consumer assault 3. Consumer assault, consumer SCIP, providing assistance to consumer 4. Consumer assault, trips, consumer SCIP Q2. Which statements are true? 1. Sept. Nov. has over a 20% increase in accident rate 2. The monthly average of staff action decreased from July November 3. Providing assistance to consumers is over 7% lower than consumer assault 4. None of the above Q3. The greatest % increase in accidents over the 6 months was in what category? 1. Repetitive movement 2. Providing assistance to consumers 3. Bending 4. Environment exposure Q4. Quarter 4 of 2006 showed the greatest percentage of decrease in which categories?? 1. Other, environment exposure 2. Blood to blood, stress 3. Trips, motor vehicle accidents 4. Consumer SCIP, Consumer lifting / transfer Chart 2.0 NYS Nurse Overtime Hours ( ) Table 2: New York State Nurse Overtime Hours -- Top 5 Agencies Using OT Percent Difference from 2003 to DOCS 192, , , ,328 24% DOH 24,819 26,752 25,960 25,785 4% SUNY 158, , , ,661 2% OMH 317, , , ,213 20% OMRDD 45,789 42,592 38,369 44,315 SOURCE: Based on data from OSC. 33

35 Chart 2.1 NYS Nurse Overtime Hours ( ) Table 2a: New York State Nurse Overtime Hours (by agency) Change & Percent Change over one State Fiscal Year (SFY 2005 to 2006) Overtime Hours Agency Change % Change DOCS 58,553 33% SED % DOH % OCFS % SUNY % OMH 121,355 47% OMRDD 5,947 15% OASAS 518 6% Total by Year 186,679 28% Learning Note: Charts 2.0 and 2.1 are related but have different purposes. Be careful to select the correct chart to answer the 4 questions below. Also be cautious of the variables of time as you answer the questions. Questions 2.0/2.1 Q1. The greatest change in overtime hours in the past 3 years occurred in what agency? 1. DOCS 3. OMH 2. SED 4. OMRDD Q2. The agency with the largest number of overtime hours in the past fiscal year is? 1. OMH 3. SED 2. DOCS 4. SUNY Q3. What is the % change in OMRDD overtime in the past 3 years? 1. 15% 3. 20% 2. -3% 4. Unable to calculate Q4. What are the top 3 agencies who have showed the most improvement in limiting overtime rates over the last year? 1. SED, DOH, SUNY 3. OMRDD, SUNY, DOH 2. DOCS, OMH, OASAS 4. None of the above. 34

36 SUMMARY: These charts may have appeared very simple as the data sets are not as large and complex as some of the charts you will view in the next section. There will also be some trick questions that will cause you to have to be mindful of negative / positive numbers, percentages and subcategories.. Spending time initially to understand the purpose of the chart and how the data is organized will help you in analyzing the correct data to make your choice. Note in some cases questions may be answered by using information from multiple charts. 35

37 Section E Continued Drawing Conclusions from Complex Tables Purpose: The charts presented in this module are the most complex representations of what you will find on the Civil Service examination. Your diligence in scanning all of the headings, subheadings and footnotes will be important as you select answers to the questions. You will also see some notes which provide insights into how to make calculations that support your answers. Rationale: Complex charts are a means of organizing large amounts of data. With the increasing demand from the public for trend analysis, variable comparisons and specific topic contrasts, these charts are increasingly used. Please note that the section posts four charts of information that are all related to US Census data and the characteristics of the US Population at or below the 2006 federal minimum wage averages. Explanation: The charts will have various questions and notes that will guide you in an analytic thought process (using the decision tree) to the correct answers. Note that the decision tree has an additional mental process that may or may not be necessary for completion. 36

38 Examples Often multiple graphs are used to depict variable relationships when you have complex raw data. The graph segments below displaying characteristics of minimum wage workers (2006 US Bureau of Census). By learning to use multiple graphs to draw conclusions, you will strengthen your skill of information analysis. NOTE: The four graphs are focused on population distribution variables and effect on workers at or below the $5.15 minimum wage in Please be thorough in reading the graph headings as well as the footnotes to find your answers. DECISION TREE The following mental decision tree is a process map that can help guide your mental thought process when interpreting more complex tables and graphs. While answers to questions may not require this process, it is created as a due diligence thought sequence which could prevent errors from erroneous assumptions and/or trick questions. There are three steps presented in process flows: the first to overview of the table, the second to interpret the question and the third to analyze and calculate. Using these three steps should help you reach toe right conclusion and answer the question correctly. 1. Overview Graph What is the purpose of the graph? What headings are presented? What footnotes are used and what is their meaning? What subheadings are presented? What groupings or classifications are made on the x and y axis? -duplication -natural groupings What data sample size is depicted? 37

39 2. Question Interpretation What is the intent of the question? Is there a quick answer just by looking at the graph? NO YES Study possibilities to eliminate potential wrong answers. Review a second time and verify if hunch is correct. Prepare paper for calculation and mark up of graph. Go over possibilities No Yes Select Answer 38

40 3. Analysis and Calculations Segregate the question s data variables from the rest of graph by points or recreating visual table or chart. Determine type of calculation required. 1. What comparisons are required? # to # + to relationships Ratios/percentages 2. What calculation type must be used in the solution? Whole numbers and fractions Addition/subtraction Multiplication/division Percentage/ratios/proportions Formulas (i.e. distance = rate x time) 3. Conduct arithmetic calculation Use clear, logical steps Record on a scrap sheet of paper Write legibly and sequentially so you can trace your work Find answer and compare to options 4. Verify your calculations and repeat if necessary 39

41 DECISION GUIDE (ADDENDUM) The Drawing Conclusions decision guide described above often requires a final step (step 4) in the decision tree. Steps 1 Overview Graph 2 Question Interpretation 3 Analysis & Calculations 4 Drawing Conclusions and answer question Based on data solution calculation what conclusions can be drawn? Points outside the limit of the charts Sufficient data exists to offer predictable trends. Do footnotes and explanations around chart provide clues? Runs about the central line of the charts Do multiple data values all on the same side of the central line exist? No Does not represent a weak sustained effect. Yes Indicates presence of an assignable cause which has weak but sustained effect. No A dominant effect does not exist. Does a single point exist outside the computed limits? Yes Indicates presence of a assignable cause with dominant effect Complex Table Questions This section consists of four tables developed by the U.S. Department of Labor Bureau of Labor Statistics. You can reference these tables and additional statistical tables at While the tables appear complex and unrelated they are all focused on comparing variables about the characteristics of minimum wage workers in We suggest you visit the decision tree guide as you answer the five questions to create a logical thought sequence which can lead to your success. Learning Note: Often the questions will not reference one particular table so you may want to write out the variables and type of outcome required. By doing this, you can find the correct table first before spending time doing calculations using incorrect variables. Also be sure to read footnotes if applicable. 40

42 The following tables are contained in this section. Remember that all relate to the characteristics of minimum wage workers. Table 1 Table 4 Table 6 Table 10 Selected characteristics (2006 annual averages) Major occupation groups (2006 annual averages) Educational attainment (2006 annual averages) Sex ( annual averages) Learning notes and help with calculations are provided after each question if extra help is needed. 41

43 Table 1. Employed wage and salary workers paid hourly rates with earnings at or below the prevailing Federal minimum wage by selected characteristics, 2006 annual averages. Number of workers Percent of workers (in thousands) Percent distribution paid hourly rates At or below $5.15 At or below $5.15 At or below $5.15 per hour per hour per hour Total paid hourly rates At $5.15 Below $5.15 Total paid hourly rates At $5.15 Below $5.15 Total Characteristic Total Total AGE AND SEX Total, 16 years and over 76,514 1, , to 24 years 16, to 19 years 5, years and over 59, Men, 16 years and over 38, to 24 years 8, to 19 years 2, years and over 29, Women, 16 years and over 38,321 1, to 24 years 8, to 19 years 2, years and over 30, RACE, SEX AND HISPANIC OR LATINO ETHNICITY White (1) 61,907 1, , Men 31, Women 30, Black or African American (1) 9, Men 4, Women 5, Asian (1) 2, Men 1, Women 1, Hispanic or Latino (1) 13, At $5.15 Below $

44 Men 7, Women 5, FULL AND PART-TIME STATUS AND SEX Full-time workers (2) 58, Men 32, Women 25, Part-time workers (2) 17,930 1, Men 5, Women 12, Detail for the race groups (white, black or African American, and Asian) will not sum to totals because data are not presented for all races. In addition, persons whose ethnicity is identified as Hispanic or Latino may be of any race and, therefore, are classified by ethnicity as well as race. 2 The distinction between full and part-time workers is based on hours usually worked. These data will not sum to totals because full or parttime status on the principal job is not identifiable for a small number of multiple jobholders. NOTE: Data exclude all the self-employed, both unincorporated and incorporated. 43

45 Table 4. Employed wage and salary workers paid hourly rates with earnings at or below the prevailing Federal minimum wage by major occupation group, 2006 annual averages Number of workers Percent of workers (in thousands) Percent distribution paid hourly rates At or below $5.15 At or below $5.15 At or below $5.15 per hour per hour per hour Occupation Total paid hourly rates Total At $5.15 Below $5.15 Total paid hourly rates Total At $5.15 Below $5.15 Total At $5.15 Below $5.15 Total, 16 years and over 76,514 1, , Management, professional, and related occupations 14, Management, business, and financial operations occupations 3, Professional and related occupations 10, Service occupations 16,992 1, , Healthcare support occupations 2, Protective service occupations 1, Food preparation and serving related occupations 6,524 1, Building and grounds cleaning and maintenance occupations 3, Personal care and service occupations 2, Sales and office occupations 21, Sales and related occupations 7, Office and administrative support occupations 13, Natural resources, construction, and maintenance occupations 10, Farming, fishing, and forestry occupations

46 Construction and extraction occupations 6, Installation, maintenance, and repair occupations 3, Production, transportation, and material moving occupations 13, Production occupations 7, Transportation and material moving occupations 6, NOTE: Data exclude all the self-employed, both unincorporated and incorporated. Dash indicates no data or data that do not meet publication criteria. 45

47 Table 6: Employed wage and salary workers paid hourly rates with earnings at or below the prevailing Federal minimum wage by educational attainment, 2006 annual averages. Number of workers Percent of workers (in thousands) Percent distribution paid hourly rates At or below $5.15 At or below $5.15 At or below $5.15 per hour per hour per hour Total paid hourly rates Total paid hourly rates At Below At Below At Below Educational attainment Total $5.15 $5.15 Total $5.15 $5.15 Total $5.15 $5.15 Total, 16 years and over 76,514 1, , Less than a high school diploma 12, Less than 1 year of high school 3, to 3 years of high school 7, years of high school, no diploma 1, High school graduates or more 63,574 1, High school graduates, no college 27, Some college or associate degree 25, Some college, no degree 17, Associate degree 7, Occupational program 4,

48 Academic program 3, College graduates, total 10, Bachelor's degree 8, Master's degree 1, Professional degree Doctoral degree Note: Data exclude all the self-employed, both unincorporated and incorporated. Dash indicates no data or data that do not meet publication criteria. 47

49 Table 10: Employed wage and salary workers paid hourly rates with earnings at or below the prevailing Federal minimum wage by sex, annual averages (Numbers in thousands) Total wage and salary workers Percent of total wage and salary workers Workers paid hourly rates Below prevailing Federal minimum wage At prevailing Federal minimum wage Total at or below prevailing Federal minimum wage Percent of hourly paid workers Year and sex Total Number BOTH SEXES ,529 51, ,916 3,997 6, ,644 51, ,087 4,686 7, ,516 51, ,513 4,311 7, ,368 50, ,348 4,148 6, ,290 51, ,077 4,261 6, ,194 54, ,838 4,125 5, ,521 55, ,639 3,899 5, (1) 96,903 57, ,599 3,461 5, ,303 59, ,468 3,229 4, ,407 60, ,319 2,608 3, ,480 62, ,372 1,790 3, (1) 104,876 63, (2) 1096 (2) 3228 (2) 5.1 (2) ,723 62, (2) 2906 (2) 5283 (2) 8.4 (2) ,668 63, ,939 2,982 4, ,101 64, ,707 2,625 4, (1) 107,989 66, ,995 2,132 4, ,038 68, ,699 1,956 3, ,960 69, (2) 1861 (2) 3724 (2) 5.4 (2) 1997 (1) 114,533 70, (2) 1764 (2) 4754 (2) 6.7 (2) 48

50 1998 (1) 116,730 71, ,834 1,593 4, (1) 118,963 72, ,194 1,146 3, (1) 122,089 73, , , ,229 73, , , ,826 72, , , (1) 122,358 72, , , (1) 123,554 73, , , (1) 125,889 75, , , ,237 76, , , The comparability of historical labor force data has been affected at various times by methodological and conceptual changes in the Current Population Survey (CPS). For an explanation, see the "Explanatory Notes and Estimates of Error" section of the February 2007 and subsequent issues of Employment and Earnings, a monthly BLS periodical. 2 Data for and reflect changes in the minimum wage that took place in those years. NOTE: The prevailing Federal minimum wage was $2.90 in 1979, $3.10 in 1980, and $3.35 in The minimum wage rose to $3.80 in April 1990, to $4.25 in April 1991, to $4.75 in October 1996, and to $5.15 in September Data exclude the unincorporated and incorporated self-employed. The presence of a sizable number of workers with reported wages below the minimum does not necessarily indicate violations of the Fair Labor Standards Act, as there are numerous exemptions to the minimum wage provisions of the law. Indeed, the relatively large number of workers with reported wages below the minimum in includes some hourly-paid workers reported as earning exactly $5.00 per hour (about 1.4 million in 1998, about 900,000 in 1999, about 600,000 in 2000, about 500,000 in 2001 and in 2002, about 350,000 in 2003 and in 2004, 300,000 in 2005, and about 250,000 in 2006); to some extent, this may reflect rounding on the part of survey respondents. 49

51 Q1. In comparing the number of full time/part time men and the number of men from each race what is the discrepancy between numbers and which conclusion statement can be drawn? Most men work full time and are then men are from various race groups men are multiple job holders race data is incomplete 4. 0 no conclusions can be made with the data Learning Notes/Calculations (Q1) Number of workers (full time/part time) Sex/Race Full time/part time Men Race Full time men 32,477 White 31,403 Part time men 5,652 African American 4,485 38,129 Asian 1,259 Hispanic 7, Q2. The percent distribution of black or African American women vs. white women that are paid hourly appears disproportionate to the percent of black or African American women vs. white women that are paid hourly rates at or below $5.15. What is the ratio and possible conclusion you can draw? 1. Ratio is 3.2% - 2.0% Data difference is not significant because of sample size and accuracy. 2. Ratio is 28.2% 8.02% Trends with the black population have indicated low wages when paid hourly 3. Ratio is 7.1% % Distribution does not parallel population ratio. 4. Ratio is 3.2% - 2.0% White women have a harder time getting better paying jobs because their part time % is so high at 4.2%. Learning Notes/Calculations (Q2) This information is from the percent distribution and percent of workers paid hourly rates for the women of each race. Black or African American Women White Women 7.1% distribution 39.9% distribution 2.0% of workers 3.2% of workers 2.0 = 28.2% 3.2 = 8.02%

52 Q3 The educational attainment Table #6 provides information on the impact high school education has on job pay. What can be implied about the level of education received and hourly rates? 1. <25% of all workers full time/part time do not have a high school diploma. 2. Of high school graduates between 1.9% and 2.9% are paid below or equal to $5.15/hr. 3. High school graduates (no college) have less than a 50% chance of earning over $5.15/hr. 4. The variations among the high school attendance: less 1 year, 1-3 years, 4 years are clear indicators of success. Learning Notes/Calculation (Q3) Less than high school diploma: 12, % all workers full time/part time no diploma 76,514 total 16 years + 2.2% less than high school diploma 16.7 less high school diploma % (less = 5.15) 3.7% paid = less 83.1 high school graduate % (less = 5.15) 1.9% paid = less 99.8 (not significant) Q4. What conclusions can be drawn from the variations in wages at or below $5.15 per hour for high school graduates (no college) and college graduates? Which statements best describes meaningful conclusions? 1. The percent of workers 1.2 /1.9= 63% is 63% more likely to receive wages at or below $5.15 if they do not get a college degree. 2. The ratio of college graduates to high school graduates (no college) is 10956:27767 or 39%. 3. The ratio of 7.5:31.6 indicates that 24% fewer workers with college degrees receive less than or equal to wages of $5.15 hour compared to workers that graduated high school, but did not attend college.. 4. The percentage of workers in the total population with wages at or below $5.15 is the same percentage as those employees with some college or Associate degree. 5. Answers 1, 2 are true. 6. Answers 1, 2, 3, 4 are true. 7. Answers 3, 4 are true. 51

53 Q5. In table 10, the numbers of employed workers are tabularized and the data presented is in thousands. What are the correct answers to the following questions? A. What is the difference between the percent of hourly paid workers at or below the Federal minimum wage in and ? 1. 12% 3. 2% 2. 8% % B. During what periods was there the largest decrease in % of hourly paid workers at or below minimum wage? C. The change in the # of workers with wages below the minimum from is represented by what ratio?

54 Glossary Tabular Reasoning: Review, Reminders, and References The overarching purpose of the use of charts and graphs is to visually summarize raw data in a format that helps the reader understand the information. The goal is to show raw data in categories that help us understand and compare / contrast variables or conditions that we could not easily understand with text. This glossary is a brief synopsis or "cheat sheet" referring to some of the most important points of the guide. Graphs / Charts Running Record Simple graph where one scale represents time and the other scale represents the measures of interest. Also called timeseries graph. Shows: Overall levels Variation over time Trends Current value in a context st Qtr 2nd Qtr 3rd Qtr 4th Qtr East Time Period Number Scale "measures interest" 53

55 Bar Charts A bar chart compares values or amounts across different categories. Shows: Values / Amounts Relationships Trends It can be horizontal or vertical Candy Ice Cream Boys Girls Categories Value Scale Fruit Ice Cream Chips Grils Boys Candy Categories Pareto Charts A pareto chart is a bar chart where the categories have been arranged from left to right according to their value. Traditionally costs are a preferred scale used. Additionally a second scale of percentage may be applied or the right side of the chart. Shows: Key areas of interest Opportunities for improvement Tracking of changes $350 $300 $250 $200 $150 $100 $50 $0 Value Scale A B C D Dollar Amount Value Scale Categories % Scale Optional 54

56 Histogram Histogram shows frequency of values "mounding" data. Shows: Frequency A B C D E Frequency East Count Scale Values Pie Charts Similar to bar chart in that they compare the amounts for various categories at a fixed point in time. The data is converted from amounts to percentages of the total amount then show as % of the pie. A% B% D% C% A% + B% + C% + D% = 100% Computation The basic arithmetic computations found in tabular reasoning are focused on measures of location. Measures of Location These measures consist of characterizing the "location" of the "mid point" of the data by averages and medians. 55