Chap 2-1

Business Statistics: A Decision-Making Approach

7th Edition

Chapter 2Graphs, Charts, and Tables –

Describing Your Data

Chap 2-2

Chapter Goals

After completing this chapter, you should be able to:

Construct a frequency distribution both manually and with a computer

Construct and interpret a histogram

Create and interpret bar charts, pie charts, and stem-and-leaf diagrams

Present and interpret data in line charts and scatter diagrams

Chapter Focus

First time trying practices using Excel Practices are simple….not strongly fun Try to be familiar with Excel

Describe data using frequency distribution and relative frequency distribution. Discrete Continuous

Present data using a chart Universal and popular way: Histogram

Chap 2-3

Variable (Data) Types

Variable(Data)

Qualitative(Categorical)

Quantitative (Numerical)

1) Discrete 2) Continuous

Chap 2-4

Chap 2-5

Data

Qualitative Data

Quantitative Data

Tabular Methods

Graphic Methods

Tabular Methods

Graphic Methods

1) Dot Plot2) Histogram3) Ogive4) Stem & Leaf Display5) Scatter Diagram

1) Frequency Distr.2) Relative/Percent Frequency Distr.3) Crosstabulation

Charts:1) Column2) Pie

1) Frequency Distr.2) Relative/Percent Frequency Distr.3) Cumulative Frequency Distr.4) Cumulative Relative/Percent Frequency Distr.5) Crosstabulation

Detail View

Chap 2-6

Frequency Distribution (FD)

It is a tabulation of the values..

Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval,

and in this way the table summarizes the distribution of values in the sample.

Number of days read Frequency

0 44

1 24

2 18

3 16

4 20

5 22

6 26

7 30

Total 200

Chap 2-7

Why Use FD?

A frequency distribution is a way to summarize data

The distribution condenses the raw data into a more useful form...

and allows for a quick visual interpretation of the data

Chap 2-8

Frequency Distribution: Discrete Data

Discrete data: possible values are countable

Example: An advertiser asks 200 customers how many days per week they read the daily newspaper.

Number of days read Frequency

0 44

1 24

2 18

3 16

4 20

5 22

6 26

7 30

Total 200

Chap 2-9

Relative Frequency

Relative Frequency: What proportion (%) is in each category?

Number of days read Frequency

RelativeFrequency

0 44 .22

1 24 .12

2 18 .09

3 16 .08

4 20 .10

5 22 .11

6 26 .13

7 30 .15

Total 200 1.00

.22200

44

22% of the people in the sample report that they read the newspaper 0 days per week

Practice

Develop FD using Discreet Data Download the “SportShoes” Excel data file

from the class website Make sure to download and SAVE the data

file. See the note (ppt).

Chap 2-10

Chap 2-11

Frequency Distribution: Continuous Data

Continuous Data: uncountable…..may take on any value in some interval

Example: A manufacturer of insulation randomly selects

20 winter days and records the daily high temperature (Temperature is a continuous variable because it could

be measured to any degree of precision desired – 98.58697 F)

24, 35, 17, 21, 24, 37, 26, 46, 58, 30,

32, 13, 12, 38, 41, 43, 44, 27, 53, 27

Chap 2-12

Grouping Data by Classes

Sort raw data from low to high (easy using Excel):12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Find range: 58 (Max) – 12 (Min) = 46 (use for class width)

Determine number of classes: Rule of thumb: between 5 and 20 Calculation of class: follow 2^k>= n (n=20) Two to the power of four and five (in Excel: 2^4=16 and 2^5=32).

Then, take 5.

Thus, there should be 5 classes.

Grouping Data by Classes

Compute class width: 10 (46/5 = 9.2 then round off 10)

Determine intervals:10, 20, 30, 40, 50 (Sometimes class midpoints are reported: 15, 25, 35, 45, 55 – if

calculation result is 13.5)

Construct frequency distribution count number of values in each class

Chap 2-13

W =

Largest Value - Smallest Value

Number of Classes

Chap 2-14

Frequency Distribution

Data from low to high:

12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Class Frequency

10 but under 19.99 3 .15 20 but under 29.99 6 .30 30 but under 39.99 5 .25 40 but under 49.99 4 .20 50 but under 59.99 2 .10 Total 20 1.00

RelativeFrequency

Frequency Distribution

0 or 12 is also OK

Chap 2-15

Histogram

0

3

6

5

4

2

00

1

2

3

4

5

6

7

5 15 25 36 45 55 More

Fre

qu

en

cy

Class Midpoints

Histogram based on FD

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

No gaps between

bars, since continuous

data

0 10 20 30 40 50 60

Class Endpoints

Chap 2-16

Histogram

The classes or intervals are shown on the horizontal axis

frequency is measured on the vertical axis Bars of the appropriate heights can be used

to represent the number of observations within each class

Such a graph is called a histogram

Chap 2-17

How Many Class Intervals?

Many (Narrow class intervals) may yield a very jagged distribution

with gaps from empty classes Can give a poor indication of how

frequency varies across classes

Few (Wide class intervals) may compress variation too much and

yield a blocky distribution can obscure important patterns of

variation.0

2

4

6

8

10

12

0 30 60 More

TemperatureF

req

ue

nc

y

0

0.5

1

1.5

2

2.5

3

3.5

4 8

12

16

20

24

28

32

36

40

44

48

52

56

60

Mo

re

Temperature

Fre

qu

en

cy

(X axis labels are upper class endpoints)

Chap 2-18

General Guidelines

Number of Data Points Number of Classes

under 50 5 - 7 50 – 100 6 - 10 100 – 250 7 - 12 over 250 10 - 20

Practice

Develop FD using continuous data Download the “Capital Credit Union” Excel

file from the class website See the note (ppt).

Chap 2-19

Joint Frequency Distribution

What does the credit card balance distribution look like from male versus female cardholder? Conventional way: Develop F.D. and Hist. for each

gender separately Better way: joint the two variables (M/F) using joint

frequency distribution…much easier to compare two different variables

See the next slide

Chap 2-20

Joint Frequency Distribution

Chap 2-21

Chap 2-22

Practice

Develop JFD and relative JFD using “Capital Credit Union” Excel file and then develop other types (i.e., charts, diagram) using “Bach, Lombard, & Wilson” Excel files

See the note (ppt).

Chap 2-23

Chap 2-24

Ogives

An Ogive is a graph of the cumulative relative frequencies from a relative frequency distribution

Ogives are sometime shown in the same graph as a relative frequency histogram

Chap 2-25

Ogives

12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Add a cumulative relative frequency column:

Class Frequency

10 but under 20 3 .15 .1520 but under 30 6 .30 .4530 but under 40 5 .25 .7040 but under 50 4 .20 .9050 but under 60 2 .10 1.00 Total 20 1.00

RelativeFrequency

Frequency Distribution

(continued)

Cumulative Relative

Frequency

Chap 2-26

Histogram

0

1

2

3

4

5

6

7

5 15 25 36 45 55 More

Fre

qu

en

cy

Class Midpoints

Ogive Example

100

80

60

40

20

0

Cum

ulat

ive

Fre

quen

cy (

%)

/ Ogive

0 10 20 30 40 50 60

Class Endpoints

Chap 2-27

Excel will show the Ogive graphically if the “Cumulative Percentage” option is selected in the Histogram dialog box

Ogives in Excel

Chap 2-28

Other GraphicalPresentation Tools

Qualitative(Categorical)

Data

Bar Chart

Stem and Leaf Diagram

Pie Charts

Quantitative(Numerical)

Data

** Try the rest of them by yourself **

Chap 2-29

Bar and Pie Charts

Bar charts and Pie charts are often used for qualitative (category) data

Height of bar or size of pie slice shows the frequency or percentage for each category

Chap 2-30

Bar Chart Example 1

Investor's Portfolio

0 10 20 30 40 50

Stocks

Bonds

CD

Savings

Amount in $1000's

(Note that bar charts can also be displayed with vertical bars)

Chap 2-31

Bar Chart Example 2

Newspaper readership per week

0

10

20

30

40

50

0 1 2 3 4 5 6 7

Number of days newspaper is read per week

Freu

ency

Number of days read

Frequency

0 44

1 24

2 18

3 16

4 20

5 22

6 26

7 30

Total 200

Chap 2-32

Pie Chart Example

Percentages are rounded to the nearest percent

Current Investment Portfolio

Savings 15%

CD 14%

Bonds 29%

Stocks42%

Investment Amount PercentageType (in thousands $)

Stocks 46.5 42.27Bonds 32.0 29.09CD 15.5 14.09Savings 16.0 14.55

Total 110 100

(Variables are Qualitative)

Chap 2-33

Tabulating and Graphing Multivariate Categorical Data

Investment in thousands of dollars

Investment Investor A Investor B Investor C Total Category

Stocks 46.5 55 27.5 129Bonds 32.0 44 19.0 95CD 15.5 20 13.5 49Savings 16.0 28 7.0 51

Total 110.0 147 67.0 324

Chap 2-34

Tabulating and Graphing Multivariate Categorical Data

Side by side charts

Comparing Investors

0 10 20 30 40 50 60

S toc k s

B onds

CD

S avings

Inves tor A Inves tor B Inves tor C

(continued)

Chap 2-35

Side-by-Side Chart Example Sales by quarter for three sales territories:

0

10

20

30

40

50

60

1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

EastWestNorth

1st Qtr 2nd Qtr 3rd Qtr 4th QtrEast 20.4 27.4 59 20.4West 30.6 38.6 34.6 31.6North 45.9 46.9 45 43.9

Chap 2-36

Stem and Leaf Diagram

A simple way to see distribution details from qualitative data

METHOD

1. Separate the sorted data series into leading digits (the stem) and the trailing digits (the leaves)

2. List all stems in a column from low to high

3. For each stem, list all associated leaves

Chap 2-37

Example:

Here, use the 10’s digit for the stem unit:

Data sorted from low to high:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

12 is shown as

35 is shown as

Stem Leaf

1 2

3 5

Chap 2-38

Example:

Completed Stem-and-leaf diagram:

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 28, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Stem Leaves

1 2 3 7

2 1 4 4 6 7 8

3 0 2 5 7 8

4 1 3 4 6

5 3 8

Chap 2-39

Using other stem units

Using the 100’s digit as the stem:

Round off the 10’s digit to form the leaves

613 would become 6 1 776 would become 7 8 . . . 1224 becomes 12 2

Stem Leaf

Chap 2-40

Line charts show values of one variable vs. time Time is traditionally shown on the horizontal axis

Scatter Diagrams show points for bivariate data one variable is measured on the vertical axis and

the other variable is measured on the horizontal axis

Line Charts and Scatter Diagrams

Chap 2-41

Line Chart Example

U.S. Inflation Rate

0

1

2

3

4

5

6

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

Year

Infl

atio

n R

ate

(%)

YearInflation

Rate1985 3.561986 1.861987 3.651988 4.141989 4.821990 5.401991 4.211992 3.011993 2.991994 2.561995 2.831996 2.951997 2.291998 1.561999 2.212000 3.362001 2.852002 1.592003 2.272004 2.682005 3.392006 3.24

Chap 2-42

Scatter Diagram Example

Production Volume vs. Cost per Day

0

50

100

150

200

250

0 10 20 30 40 50 60 70

Volume per Day

Cos

t per

Day

Volume per day

Cost per day

23 125

26 140

29 146

33 160

38 167

42 170

50 188

55 195

60 200

Chap 2-43

Types of Relationships

Linear Relationships

X X

YY

Chap 2-44

Curvilinear Relationships

X X

YY

Types of Relationships(continued)

Chap 2-45

No Relationship

X X

YY

Types of Relationships(continued)

Chap 2-46

Chapter Summary

Data in raw form are usually not easy to use for decision making -- Some type of organization is needed:

Table Graph

Techniques reviewed in this chapter: Frequency Distributions, Histograms, and Ogives Bar Charts and Pie Charts Stem and Leaf Diagrams Line Charts and Scatter Diagrams