chapter 3 graphical displays of data

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DoingDoing Statistics for BusinessStatistics for Business Data, Inference, and Decision Making

Marilyn K. PelosiTheresa M. Sandifer

Chapter 3Chapter 3Graphical Graphical

Displays of Data Displays of Data

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Doing Statistics for Business

Chapter 3 Objectives Graphical Methods for Qualitative Data:

Frequency Tables

Bar Charts

Pie Charts Graphical Methods for Quantitative Data:

Frequency tables

Histograms

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Chapter 3 Objectives (con’t) Other Graphical Methods:

Dotplots

Pareto Diagrams

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A Frequency Table or FrequencyDistribution is a table containing eachcategory, value or class of values that avariable might have and the number of times that each one occurs in the data.The frequency of the ith class is denotedf.

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Figure 3.1 A Frequency Table

Category Frequency

Category 1 f1

Category 2 f2

.

.

.

.

.

.

Total n

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The Relative Frequency of a classification isthe number of times an observation falls intothat classification represented as a portion ofthe total number of observations. It can be expressed as a fraction, decimal, or percentage.

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TRY IT NOW!Student GradesCreating a Frequency Table

A professor in an Introductory Statistics course knows that while students

dread taking the course, they also have unusually high expectations for

their performance. She surveys (anonymously, of course) her students

and asks them what grade they expect to get in the course.

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TRY IT NOW!Student GradesCreating a Frequency Table (con’t)The raw data are:

A C B A A B B

B A B A A C B

B A F C B D CB B D B A B A

Make a frequency table for the data. Include both frequencies and relativefrequencies.

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The Cumulative Relative Frequency of aclass is the sum of the relative frequencies ofall classes at or below that class represented asa portion of the total number of observations.It can be expressed as a fraction, decimal, orpercentage.

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TRY IT NOW!New Product Survey

Cumulative Relative FrequenciesA marketing research firm conducted a survey of consumers who

invariably use a particular brand of of bath soap. The consumers were

given a competitor’s version of the same product with non-allergenic

enhancements and asked whether they would consider buying the new

product. Their answers were given on a scale of 1 to 5 where 1 = would

not ever buy this product and 5 = will buy this product immediately.

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Cumulative Relative Frequencies (con’t)The raw data from the survey are given below:

5 4 1 4 2 23 1 4 4 2 43 1 3 3 5 44 4 2 3 2 54 3 4 4 1 5

Create a frequency table for the data that includes both frequency andcumulative relative frequency.

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Cumulative Relative Frequencies (con’t)

Which ratings indicate a negative attitude toward the new product? What percentage of people surveyed had a negative attitude?

Which rating indicates a neutral attitude? What percentage of the people

surveyed had a neutral attitude?

Which ratings indicate a positive attitude? What percentage had apositive attitude?

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M in im u m M a x im u m

N u m b er o f c la s s e s( s tep s ) to co v e r th e

in te rv a l = n

S iz e o f ea ch c la s s =

M a x im u m M in im u m

o f c la s s e s

#

Figure 3.2 Number of Classes & Class Interval for Continuous Data

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Figure 3.3 Microsoft Excel Frequency TableIn Excel, the number in the Bin column is the highest number that is

included in the interval, so the first bin is all numbers less than and

including 29.50, and the last bin is all numbers greater than 81.58.

Bin Frequency Cumulative %29.50 1 3.3342.52 4 16.6755.54 4 30.0068.56 10 63.3381.58 6 83.33More 5 100.00

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TRY IT NOW!Assignment Times

Creating a Frequency Table forContinuous Data

The instructor for an introductory statistics class wonders about thecomplaints that she is hearing about the time it takes to complete acomputer assignment. The assignments are designed to be done in about25 minutes. She asks the members of the class to time how long it takesto do the next assignment and to hand the data in with the assignment.

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TRY IT NOW!Assignment TimesCreating a Frequency Table forContinuous Data (con’t)The data, in minutes, she obtains are:

24.8 27.0 27.9 30.4 33.424.8 27.2 27.9 31.1 33.924.8 27.4 28.2 31.4 35.326.0 27.4 29.4 32.4 35.726.0 27.4 29.6 33.1 36.326.1 27.6 29.8 33.2 40.4

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TRY IT NOW!Assignment TimesCreating a Frequency Table forContinuous Data (con’t)

Approximately how many classes should the frequency table have?

What should the class width be?

Create a frequency table for the data.

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A Bar Chart represents thefrequency or relativefrequency from the table inthe form of a rectangle or bar.

Class Year of Students in Introductory Statistics

0

2

4

6

8

10

12

Freshman

Sophomore

Junior

SeniorClass

Year

Number ofStudents

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TRY IT NOW!Student Grades

Creating a Bar Chart

The instructor who surveyed her students about expected grades wants to

create a bar chart from the data.

The frequency table for data is

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TRY IT NOW!Student GradesCreating a Bar Chart (con’t)

Create a bar chart for the data using relative frequency on the y axis. Besure to label the axes and include an appropriate title.

Grade Frequency Relative Frequency(%)

A 9 32.1B 12 42.9C 4 14.3D 2 7.1F 1 3.6

Total 28 100

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A Pareto Diagram is a bar chart in which the categories are plotted in order of decreasing relative frequency. In addition to the bars, the cumulative relative frequency of the categories is plotted on the same graph.

% of Complaints

Pareto Diagram - Customer Complaints

0.00%

20.00%

40.00%

60.00%

80.00%

Dispensing Packaging Miscounts Softness Odor Pricing

Complaint Category

.00%

20.00%

40.00%

60.00%

80.00%

100.00%

Cumulative % of Complaints

Relative Frequency

Cumulative %

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A Pie Chart represents data

in the form of slices or

sections of a circle. Each

slice represents a category

and the size of the slice is

proportional to the relative

frequency of the category.

Class Year of Introductory Statistics Students

Freshman14%

Sophomore43%Junior

7%

Senior36%

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Cumulative Relative Frequencies

The marketing research firm that is conducting a survey about customer

attitudes toward a new brand of soap would like to look at its data

graphically. The frequency table for the data is shown on the following

slide:

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Cumulative Relative Frequencies (con’t)

Create a relative frequency histogram for the data.

Rating Frequency Relative Frequency0 2 6.7%1 3 10.0%2 4 13.3%3 6 20.0%4 11 36.7%5 4 13.3%

Total 30 100.0%

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In a Dot Plot, each observation is plotted as a point on a

single, horizontal axis. The axis is scaled so that each of the

data points can be located uniquely on the axis. When there

is more than one observation with the same value the points

are “stacked” on top of each other.

---+---------+---------+---------+---------+---------+---People 10.0 12.0 14.0 16.0 18.0 20.0

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The Shape of a set of data describes how the data

are spread out around the center with respect to

the symmetry or skewness of the data.

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The Variability of a set of data describes how the

data are spread out around the center with respect

to the smoothness and magnitude of the

variation.

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When data are evenly

spread out on both sides

of the center, we

describe the distribution

of the data as symmetric.

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When data are not evenly spread out on either

side of the center then we refer to the

distribution as being skewed.

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Creating a Frequency Table forContinuous Data

The instructor for the introductory statistics class wants to see the data she

has collected on the amount of time it took the students to do the

assignment graphically.

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TRY IT NOW!Assignment TimesCreating a Frequency Table forContinuous Data (con’t)

The frequency distribution for the data is:

Time Frequency RelativeFrequency

22.70 < x <26.22 6 20.0%26.22 < x < 29.74 11 36.7%29.74 < x < 33.26 7 23.3%33.26 < x < 36.78 5 16.7%36.78 < x < 40.30 0 0.0%40.30 < x < 43.82 1 3.3%

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Creating a Frequency Table forContinuous Data (con’t)Create a relative histogram for the data.

Use the histogram to describe the distribution of the times the students

took to complete the assignment.

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Discovery Exercise 3.1Thinking About Variability

A manufacturer of compact disc uses two different suppliersfor the jewel boxes used to hold the discs. There have been problems withthese boxes in the past. The inside width of the jewel box has criticalspecifications of 119.0 0.2 mm. If the case is too narrow the disc will notfit in it and if it is too wide, the front label insert slips around. Because itis time to renew the purchasing contracts for the jewel boxes, the CDmanufacturer decides to take a look at a sample of the boxes from eachsupplier.

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The data (in mm) for each source is:

Make a relative frequency histogram of the data for each supplier

Supplier A118.7 118.9 119.0 119.1 119.2118.8 119.0 119.0 119.1 119.2118.8 119.0 119.0 119.1 119.2118.9 119.0 119.1 119.2 119.2118.9 119.0 119.1 119.2 119.3

Supplier B118.8 118.8 118.9 118.9 118.9118.8 118.8 118.9 118.9 119.0118.8 118.8 118.9 118.9 119.0118.8 118.8 118.9 118.9 119.0118.8 118.9 118.9 118.9 119.1

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Describe the distribution of jewel box widths for each supplier

and compare them.

Your company has decided to single source their supply of jewel boxes.

The purchasing agent in charge of the accounts argues that supplier B

should not get a renewed contract since he observes that the jewel boxes

from that source are not centered at the target specification of 119.0 mm

while the jewel boxes from supplier A are right on target.

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Can you explain to him why, although his observation is true,

his decision to use Supplier B is not necessarily correct? What factor

has he failed to consider?

Which supplier would you recommend they use? Write a short memo to

the manager with your recommendation and your supporting reasons.

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The basics of creating a chart in Excel,

using the Chart Wizard.

1. Highlight the data (Frequency table) that you want to graph.

2. Invoke the Chart Wizard by clicking on the icon on the toolbar.

3. Follow the directions and hints from the Chart Wizard.

4. Edit the graph to include any other features or changes you want.

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Figure 3.15 Finished Excel Column Chart

Aluacha Balaclava College - Faculty Rank

67

77

8

55

0

10

20

30

40

50

60

70

80

90

Associate Assistant Instructor Professor

Rank

Num

ber

of F

acul

ty

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Figure 3.16 Formatting the Pie Chart

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Figure 3.19 Pareto Diagram in Excel

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The basics of creating a Frequency Table

in Excel.

1. Highlight the data for which you want to create the frequency table.

2. Invoke the Pivot Tablet Wizard in Excel by using the

Data > Pivot Table Report Menu.

3. Follow the directions that the Pivot Table Wizard gives you.

4. Copy or Edit the pivot table to include any changes you want.

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Figure 3.23 Finished Pivot Table

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The basics of creating Histograms in Excel.

1. From the Data Analysis dialog box, select Histogramand click OK. The Histogram dialog box will open.2. Position the cursor in the Input Range text box and highlight the range that contains the data, B1:B208.3. Click the checkbox for Labels since the range contains the variable name.4. Excel calls the class intervals for continuous data Bins. Leave the Bin text box empty this time and let Excel pick the class intervals.

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The basics of creating Histograms in Excel. (con’t)

5. Click the radio button for Output Range, position the cursor in the text box, and click on the cell where you want the top left corner of the output to appear.

6. Finally, click the checkbox for Chart Output. The completed dialog box appears in Figure 3.25 (Slide 43).

7. Click OK and the output will appear as shown in Figure 3.26 (Slide 44).

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Figure 3.25 Completed Histogram Dialog Box

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Figure 3.26 Output from Histogram Tool

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Figure 3.31 Completed Histogram

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Chapter 3 Summary

In this chapter you have learned: The purpose of descriptive statistics is to turn data

into information. Qualitative data can be displayed using bar charts

or pie charts. Quantitative data are usually displayed using a

histogram or dotplot.

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Chapter 3 Summary (con’t) Graphical displays of data can be used to describe

data in terms of center, shape, and variability. Computer software packages, such as Excel,

greatly enhance the quality of the finished graphs.

chapter 3 graphical displays of data

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