MyStatLab • We will use this program to assign and grade

homework, for computations (StatCrunch), and

for its various multimedia tools such as its Java

Applets.

• Today, Mr. Chris Delaney from Pearson

Publishing will explain how you get registered into

the MyStatLab system so that you can begin to

do homework and take advantage of its learning

aids.

• Tomorrow in recitation, hardcopy of the

registration directions will be handed out.

Statistics for Business and

Economics

Chapter 2: Secs 1, 2

Methods for Describing

Sets of Data

Contents

Sec 2.1 Describing Qualitative Data (minimal

read: pp. 40-42.)

Sec 2.2 Graphical Methods for Describing

Quantitative Data (minimal read:

pp. 51-57.)

2.1

Describing Qualitative Data

MyStatLab Exercises 1, 2

(Due 9/11/13, 11:59 pm)

Key Terms A class is one of the categories into which qualitative data can be classified.

The class frequency is the number of observations in the data set falling into a particular class.

The class relative frequency is the class frequency divided by the total numbers of observations in the data set.

The class percentage is the class relative frequency multiplied by 100.

Data Presentation

Data

Presentation

Qualitative

Data

Quantitative

Data

Summary

Table

Stem-&-Leaf

Display

Frequency

Distribution

Histogram Bar

Graph

Pie

Chart

Pareto

Diagram

Dot

Plot

Data Presentation

Data

Presentation

Qualitative

Data

Quantitative

Data

Summary

Table

Stem-&-Leaf

Display

Frequency

Distribution

Histogram Bar

Graph

Pie

Chart

Pareto

Diagram

Dot

Plot

Summary Table

1. Lists categories & number of elements in category

2. Obtained by tallying responses in category

3. May show frequencies (counts), % or both

Row Is

Category Tally:

|||| ||||

|||| ||||

Major Count

Accounting 130

Economics 20

Management 50

Total 200

Data Presentation

Data

Presentation

Qualitative

Data

Quantitative

Data

Summary

Table

Stem-&-Leaf

Display

Frequency

Distribution

Histogram Bar

Graph

Pie

Chart

Pareto

Diagram

Dot

Plot

0

50

100

150

Acct. Econ. Mgmt.

Major

Bar Graph

Vertical Bars

for Qualitative

Variables

Bar Height

Shows

Frequency or %

Zero Point

Percent

Used

Also

Equal Bar

Widths

Fre

qu

en

cy

Data Presentation

Data

Presentation

Qualitative

Data

Quantitative

Data

Summary

Table

Stem-&-Leaf

Display

Frequency

Distribution

Histogram Bar

Graph

Pie

Chart

Pareto

Diagram

Dot

Plot

Econ.

10%

Mgmt.

25%

Acct.

65%

Pie Chart

1. Shows breakdown of

total quantity into

categories

2. Useful for showing

relative differences

3. Angle size

• (360°)(percent)

Majors

(360°) (10%) = 36°

36°

Data Presentation

Data

Presentation

Qualitative

Data

Quantitative

Data

Summary

Table

Stem-&-Leaf

Display

Frequency

Distribution

Histogram Bar

Graph

Pie

Chart

Pareto

Diagram

Dot

Plot

Pareto Diagram Like a bar graph, but with the categories arranged by

height in descending order from left to right.

0

50

100

150

Acct. Mgmt. Econ.

Major Vertical Bars

for Qualitative

Variables

Bar Height

Shows

Frequency or %

Zero Point

Percent

Used

Also

Equal Bar

Widths

Fre

qu

en

cy

Summary Bar graph: The categories (classes) of the qualitative variable are represented by bars, where the height of each bar is either the class frequency, class relative frequency, or class percentage.

Pie chart: The categories (classes) of the qualitative variable are represented by slices of a pie (circle). The size of each slice is proportional to the class relative frequency.

Pareto diagram: A bar graph with the categories (classes) of the qualitative variable (i.e., the bars) arranged by height in descending order from left to right.

Thinking Challenge

You’re an analyst for IRI. You want to show the

market shares held by Web browsers in 2006.

Construct a bar graph, pie chart, & Pareto diagram

to describe the data.

Browser Mkt. Share (%)

Firefox 14

Internet Explorer 81

Safari 4

Others 1

0%

20%

40%

60%

80%

100%

Firefox Internet

Explorer

Safari Others

Bar Graph Solution* M

ark

et S

ha

re (

%)

Browser

Pie Chart Solution*

Market Share

Safari, 4%

Firefox,

14%

Internet

Explorer,

81%

Others,

1%

Pareto Diagram Solution*

0%

20%

40%

60%

80%

100%

Internet

Explorer

Firefox Safari Others

Ma

rket

Sh

are

(%

)

Browser

2.2

Graphical Methods for Describing

Quantitative Data

MyStatLab Exercises 18, 19, 20, 21

(Due 9/11/13, 11:59 pm)

Data Presentation

Data

Presentation

Qualitative

Data

Quantitative

Data

Summary

Table

Stem-&-Leaf

Display

Frequency

Distribution

Histogram Bar

Graph

Pie

Chart

Pareto

Diagram

Dot

Plot

Dot Plot

1. Horizontal axis is a scale for the quantitative variable,

e.g., percent.

2. The numerical value of each measurement is located

on the horizontal scale by a dot.

Data Presentation

Data

Presentation

Qualitative

Data

Quantitative

Data

Summary

Table

Stem-&-Leaf

Display

Frequency

Distribution

Histogram Bar

Graph

Pie

Chart

Pareto

Diagram

Dot

Plot

Stem-and-Leaf Display

1. Separate each observation

into stem value and leaf

value

• Stems are listed in

order in a column

• Leaf value is placed in

corresponding stem

row to right of bar

2. Ordered Data: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41

26

2 144677

3 028

4 1

Stem-and-Leaf Display (Double Stems)

1. Separate each observation

into stem value and leaf

value. Here we use each

stem digit twice to capture

greater detail in the

distribution of the data.

For example, use one stem

of value 2 to hold leaves

from {0,1,2,3,4} and the

other to hold leaves from

{5, 6, 7, 8, 9}.

2. Ordered Data: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41

2 677

3 02

4 1

4

3

2

8

144

Data Presentation

Data

Presentation

Qualitative

Data

Quantitative

Data

Summary

Table

Stem-&-Leaf

Display

Frequency

Distribution

Histogram Bar

Graph

Pie

Chart

Pareto

Diagram

Dot

Plot

Frequency Distribution

Table Steps

1. Determine range

2. Select number of classes

• Usually between 5 & 15 inclusive

3. Compute class intervals (typically equal width)

4. Determine class boundaries (limits)

5. Compute class midpoints

6. Count observations & assign to classes

Frequency Distribution Table

Example

Raw Data: 24, 26, 24, 21, 27 27 30, 41, 32, 38

Boundaries (Lower + Upper Boundaries) / 2

Width

Class Midpoint Frequency

15.5 – 25.5 20.5 3

25.5 – 35.5 30.5 5

35.5 – 45.5 40.5 2

Relative Frequency &

% Distribution Tables

Percentage

Distribution

Relative Frequency

Distribution

Class Prop.

15.5 – 25.5 .3

25.5 – 35.5 .5

35.5 – 45.5 .2

Class %

15.5 – 25.5 30.0

25.5 – 35.5 50.0

35.5 – 45.5 20.0

Data Presentation

Data

Presentation

Qualitative

Data

Quantitative

Data

Summary

Table

Stem-&-Leaf

Display

Frequency

Distribution

Histogram Bar

Graph

Pie

Chart

Pareto

Diagram

Dot

Plot

0

1

2

3

4

5

Histogram

Frequency

Relative

Frequency

Percent

0 15.5 25.5 35.5 45.5 55.5

Bars

Touch

Class Freq.

15.5 – 25.5 3

25.5 – 35.5 5

35.5 – 45.5 2

Count