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Doing Statistics for Business Data, Inference, and Decision Making Marilyn K. Pelosi Theresa M. Sandifer. Chapter 3 Graphical Displays of Data. Doing Statistics for Business. Chapter 3 Objectives Graphical Methods for Qualitative Data: Frequency Tables Bar Charts Pie Charts - PowerPoint PPT Presentation
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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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Doing Statistics for Business
Chapter 3 Objectives (con’t) Other Graphical Methods:
Dotplots
Pareto Diagrams
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Doing Statistics for Business
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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Doing Statistics for Business
Figure 3.1 A Frequency Table
Category Frequency
Category 1 f1
Category 2 f2
.
.
.
.
.
.
Total n
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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
TRY IT NOW!New Product Survey
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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Doing Statistics for Business
TRY IT NOW!New Product Survey
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
TRY IT NOW!New Product Survey
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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Doing Statistics for Business
TRY IT NOW!New Product Survey
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
TRY IT NOW!Assignment Times
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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Doing Statistics for Business
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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Doing Statistics for Business
TRY IT NOW!Assignment Times
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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Doing Statistics for Business
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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Doing Statistics for Business
Discovery Exercise 3.1Thinking About Variability
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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Doing Statistics for Business
Discovery Exercise 3.1Thinking About Variability
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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Doing Statistics for Business
Discovery Exercise 3.1Thinking About Variability
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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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
Figure 3.16 Formatting the Pie Chart
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Doing Statistics for Business
Figure 3.19 Pareto Diagram in Excel
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Doing Statistics for Business
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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Doing Statistics for Business
Figure 3.23 Finished Pivot Table
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Doing Statistics for Business
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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Doing Statistics for Business
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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Doing Statistics for Business
Figure 3.25 Completed Histogram Dialog Box
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Doing Statistics for Business
Figure 3.26 Output from Histogram Tool
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Doing Statistics for Business
Figure 3.31 Completed Histogram
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Doing Statistics for Business
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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Doing Statistics for Business
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.