# Business Statistics: Visualizing Profit and Performance

This chapter from the Complete Idiot's Guide to Business Statistics gives you some handy hints on how to turn your raw data into useful graphs and charts.
This chapter is from the book

### This chapter is from the book 

In This Chapter

• Making data visually understandable

• Representing data in useful ways

• Displaying data in various charts, graphs, and plots

• Understanding the concept of "skew"

If you've been given a list of daily numbers for all the sales in the country over the last two work weeks for your new battery product, you'd have little hope of understanding the numbers by themselves. You need to summarize the numbers in some way. Suppose you have observations of the following sales numbers over ten days (two work weeks) for boxes of batteries sold by your western regional distributors:

49, 37, 89, 63, 65, 55, 66, 104, 41, 66

This list of numbers is an example of raw data, as you might remember from Chapter 1, "Statistics and Business Go Hand in Hand." Raw data are numbers that haven't been transformed with other statistical (mathematical) operations. How can you see underlying patterns in a row of naked numbers? There must be a more productive way to view the information.

Reduce the Risk

Before any statistical calculation—even the simplest—is performed, your data should be tabulated, graphed, or plotted.

## Turning Raw Data into Information

Raw numbers need to be organized in a way that makes them understandable. You could simply state that on Monday of the first week we sold 49 boxes of batteries, on Tuesday 37, on Wednesday 89, and so on—but there's got to be a better way to represent and understand the data than a simple narrative. There are three main ways to present raw statistical data such as this: in tables, graphs, and charts. I'll start with tables, move on to graphs, and then discuss pie charts (which look exactly like pizza pies without the pepperoni) and other charting options.

### Using Tables

Tables provide an easy format to present raw data in an orderly way that (hopefully) also is easy to read. However, if tables contain hundreds or thousands of numbers, they might not be too easy to understand. Things must be summarized (which I'll talk about later in this chapter). You'll be working with simple tables for now. The following table simply displays the number of boxes of sales for each day of the two weeks using the same data from the beginning of this chapter.

#### Western Region Battery Sales in Boxes for Two Weeks

Days

Week One

Week Two

Monday

49

55

Tuesday

37

66

Wednesday

89

104

Thursday

63

41

Friday

65

66

Totals for the Week

303

332

Sometimes you might want to use tables to make comparisons. Suppose you want to compare the sales of the Western and Eastern regions. Here's a table that represents and compares two weeks of sales both:

#### Western and Eastern Region Battery Sales by Boxes for Two Weeks

Days

Week One Western

Week One Eastern

Week Two Western

Week Two Eastern

Monday

49

102

55

97

Tuesday

37

95

66

89

Wednesday

89

37

104

42

Thursday

63

41

41

45

Friday

65

55

66

66

Totals for the Weeks

303

330

332

339

You can graph the numbers with dots for each number or actually connect the dots (as shown in later examples in this chapter) with a line that makes a pattern of what is happening with the data. One of the most basic (and important) statistical tables is the frequency table. You can construct this type of table by dividing scores or instances into intervals, and counting the number of scores or instances in each interval. An interval or instance can be 1, but in large frequency tables the frequencies likely will be put into groups such as all frequencies ranging from 1-5, 6-10, and so on. The actual number and percentage of scores in each interval typically are displayed.

Cumulative frequencies also are displayed in a frequency table. A frequency table for the range of chess moves for the players in a chess tournament is provided in the following table as an example of a typical frequency table.

#### Chess Moves by Number of Players: Cumulative Frequencies

Lower
Limit

Upper
Limit

Players
Count

Cumulative
Count of
Players

Percentage

Cumulative
Percentage

25

35

1

1

5

5

35

45

3

4

20

25

55

65

5

10

50

75

75

85

9

19

45

95

85

95

1

20

5

100

Note: Values are > lower limit and < upper limit of moves per game.

You'll probably agree that, simple or complex, tables generally are boring. However, you can add color and dimension to them with today's software—even Microsoft Word 2000 will enable you to do that. Even better than playing with various designs for the tables, you can turn the same data into more interesting graphs and plots that help you interpret the data quite easily.

### Using Pie Charts

Pie charts, also called graphs, are a good way to show the relative percentages of a total amount that has been sold, delivered, or manufactured in a business—among other business uses. The following figure shows a simple pie chart that represents the Western region's first week of sales of boxes of batteries.

Figure 3.1 Example of a pie chart.

Line graphs (also called plots) are another simple way of representing data. The following figure shows a line graph that represents the first week of sales for both the Western and Eastern regions on one graph. You can see that even though the total sales by week is very similar—that days on which the most boxes are sold vary. This is the power of graphing raw data—the ability to see things more easily than you can see them in tables or as raw data.

Figure 3.2 Graph of Western and Eastern regional sales for one week.

A polygon plot is skewed if one of its tails is longer than the one in the other direction. The first graph shown in the first of the following three figures has a positive skew. This means it has a long tail in the positive direction. The distribution graph shown in the second of the following figures has a negative skew because it has a long tail in the negative direction. Finally, the third distribution, shown in the third figure is symmetric and has no skew. The tails are the same length and shape on each side. Distributions with positive skew sometimes are called "skewed to the right;" distributions with negative skew are called "skewed to the left."

This is a little bit confusing. Remember, it's the long tail—not the big area of the plot—that determines the direction of the skew. You'll be learning more about skewed distributions in Chapter 6, "Solving Problems with Curves and z-Scores."

Figure 3.3 Graph of positive skew.

Figure 3.4 Graph of negative skew.

Figure 3.5 Graph of symmetric distribution (no skew).

### Using Histograms

You can create many different charts and graphs from a frequency table. A histogram is one of the basic graphs that can be constructed from a frequency table. The intervals are shown on the X axis; the number of scores in each interval is represented by the height of a rectangle located above the interval. The following chart is a histogram for the number of moves by the players in a chess tournament.

Figure 3.6 Histogram of chess moves by number of players in a tournament with that frequency per game.

Histograms vary based on the class intervals you use. For example, a histogram of the sales of your boxes of batteries by quarter might look much different than those by month. This is because the shapes of histograms will vary depending on the choice of the size of the intervals. In the first quarterly histogram, I've used intervals of 500 boxes on the X axis. In the second histogram on the same data, I've used intervals of 100 boxes on the X axis. For the monthly histogram, I'm using an interval of 10. Look at the following examples to see how the histograms change based on the size of the intervals.

#### Monthly Battery Cases Sold in 2002

 Jan 700 Feb 800 March 700 April 600 May 757 June 550 July 867 August 1067 Sept 883 October 567 November 933 December 683

#### Sales Boxes Sold by Quarter

 Qtr 1 2200 Qtr 2 1907 Qtr 3 2817 Qtr 4 2183

Figure 3.7 Histograms of quarterly sales of batteries.

Figure 3.8 Histogram of monthly sales of batteries with 10 unit intervals.

You can see how the length of observation and interval can affect someone's perception of sales during the various months and quarters in 2002. Thus, choosing the interval is important in developing histograms. Here are some helpful steps for you to follow:

• Use intervals of equal length with midpoints at convenient round numbers.

• For a small data set, use a small number of intervals.

• For a large data set, use more intervals.

Another way to display frequencies is with the cumulative frequency distribution. This is a plot or histogram of the number of observations falling on, in, or below an interval. The graph shown in the following figure is a cumulative frequency distribution in the form of a histogram of the scores on a single statistics test. Forty students took the test. The X axis shows various intervals of scores (the interval labeled 35 includes any score from 32.5 to 37.5). The Y axis shows the number of students scoring in the interval or below the interval.

Any cumulative frequency distribution can be displayed as either the actual frequencies at or below each interval (as shown here) or the percentage of the scores at or below each interval. A cumulative frequency distribution can be a histogram, as shown in the next figure, or a polygon plot as shown in the following figure.

Figure 3.9 Cumulative scores on a statistics test for forty students.

There are many ways to display frequencies in a series of related observations, such as people attending the doctor's office over a period of a month, numbers of people riding on the train each month over a year, or the number of boxes of batteries sold each month in a year. One way of displaying the cumulative frequencies over a period is using a frequency polygon as another graphical display of a frequency table.

Figure 3.10 The cumulative frequency of batteries sold over a period of twelve months.

In a frequency polygon the intervals are shown on the X axis; the number of scores, observations, or counts in each interval is represented by the height of a point located above the middle of the interval. The points are connected so that with the X axis they form a polygon, which sometimes looks like a mountain or two mountains; other times it looks like a hill or bell shape, depending on the way the frequencies distribute themselves on the plot. You'll see a lot of frequency diagrams in other chapters.

### Using the Bar Graph

A bar graph is much like a histogram, except the columns are separated from each other by a short distance. Bar graphs are commonly used for qualitative variables such as colors, brand names of cars, or other such nominal data. The following chart is a bar graph of the colors of toy wagons sold by color.

Figure 3.11 Sample of a simple bar chart.

### InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.

## Overview

Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

## Collection and Use of Information

To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

### Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

### Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

### Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

### Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

### Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

### Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

## Other Collection and Use of Information

### Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

### Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

### Do Not Track

This site currently does not respond to Do Not Track signals.

## Security

Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

## Children

This site is not directed to children under the age of 13.

## Marketing

Pearson may send or direct marketing communications to users, provided that

• Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
• Such marketing is consistent with applicable law and Pearson's legal obligations.
• Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
• Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

## Correcting/Updating Personal Information

If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

## Choice/Opt-out

Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

## Sale of Personal Information

Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

## Supplemental Privacy Statement for California Residents

California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

## Sharing and Disclosure

Pearson may disclose personal information, as follows:

• As required by law.
• With the consent of the individual (or their parent, if the individual is a minor)
• In response to a subpoena, court order or legal process, to the extent permitted or required by law
• To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
• In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
• To investigate or address actual or suspected fraud or other illegal activities
• To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
• To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
• To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.