Lecture Statistical techniques in business and economics - Chapter 2: Describing data: frequency distribution and graphic presentation

When you have completed this chapter, you will be able to: Organize raw data into frequency distribution; produce a histogram, a frequency polygon, and a cumulative frequency polygon from quantitative data; develop and interpret a stem-and-leaf display; present qualitative data using such graphical techniques such as a clustered bar chart, a stacked bar chart, and a pie chart; detect graphic deceptions and use a graph to present data with clarity, precision, and efficiency.

Organize  raw data  into frequency distribution

a cumulative frequency polygon from 

quantitative data        Develop   and interpret  a stem­and­leaf display

When you have completed this chapter, you will be able to:

2 ­ 4

Class Midpoint or Class Mark:

A point that  divides   a class  

into  two equal parts , i.e. the 

The  class interval  is obtained by  subtracting the lower limit   of 

a class   from the lower limit of the next class , e.g.

5

17.5 22.5 27.5 32.5

18.9,  10.3,  26.1,  15.7,  14.0,  17.8,  33.8,  23.2, 12.9,  27.1,   16.6.      

Organize the data into a frequency distribution.

Set up  the individual class limits.

Tally  the items into the classes.

Count  the number of items in each class.

Decide   how many classes  you wish to use

Use the  2  to the  K  rule.

Choose  k  so that  2  raised to the  power of   k  is  greater 

Determine  the  class width

Generally, the  class width  should   be 

10.0 – 14.9 15.0 – 19.9 20.0 – 24.9 25.0 – 29.9 30.0 – 34.9

Lower class limits   will be:   10, 15, 20, etc.

Lower class limits   will be:   10, 15, 20, etc.

Classes or

10.0  to  under 15

15.0  to  under   20 20.0  to  under 25

25.0  to  under 30

30.0  to  under 35

10.0  to  under 15

15.0  to  under   20 20.0  to  under 25

15.0,  23.7,  19.7,  15.4,  18.3,   23.0,  14.2,  20.8,  13.5,  

20.7,  17.4,  18.6,  12.9,  20.3,   13.7,  21.4,  18.3,  29.8,  

17.1,  18.9,  10.3,  26.1,  15.7,   14.0,  17.8,  33.8,  23.2,  

12.9,  27.1,  16.6.      

15.0,  23.7,  19.7,  15.4,  18.3,   23.0,  14.2,  20.8,  13.5,  

20.7,  17.4,  18.6,  12.9,  20.3,   13.7,  21.4,  18.3,  29.8,  

17.1,  18.9,  10.3,  26.1,  15.7,   14.0,  17.8,  33.8,  23.2,  

12.9 12.9

Find Find

30

1 1

30

5

…will give you a different distribution, e.g.

Construct a Frequency Distribution

Using E xcel

Click on 

Frequency  Distributions

See…

Using

Click on  Quantitative Click on 

Quantitative

See…

Using

Relative Frequency 

Distribution

  7/30 = 0.2333   3/30 = 0.10

 1/30 = 0.0333 

30/30 =1

1/30 = 0.0333  12/30 = 0.40  10/30 = 0.3333 

  1/30 = 0.0333   1/30 = 0.0333 

30/30 =1

1 12 10

1 1

5   5/30 = 0.1666 

A student achieved the following  scores on the twelve accounting 

Stem

69

78   82 91

7 8 9

 A       

on this test?

How many  students  earned an  

What is the  most common   letter grade  earned?

Grading

Graphic  Presentation of a 

Frequency  Distribution

Graphic  Presentation of a 

Frequency  Distribution

Graphic Presentation of a  Frequency Distribution

Graphic Presentation of a  Frequency Distribution

The three commonly used graphic forms are:

Histograms  Frequency Polygons or Line Charts Cumulative Frequency Distributions 

The  three commonly used graphic forms  are:

Histograms  Frequency Polygons  or Line Charts

Cumulative Frequency Distributions  

Graphic Presentation of a  Frequency Distribution

Graphic Presentation of a  Frequency Distribution

0     10     15     20     25     30     35       

14 12 10 8 6 4 2

7.5 12.5 17.5 22.5 27.5

0 5 10 15 20 25 30 35

how many  or  what 

proportion   of  the  data 

values   are   below  or  above    

      a certain 

value.

Graphic Presentation of a  Frequency Distribution Graphic Presentation of a  Frequency Distribution

Making a  Histogram      

       in Excel

The upper limits of the classes you have  determined

determined

Using

Complete INPUTTING of DATA Complete INPUTTING of DATA       must now be entered from       

Using

Edit  the  size of the 

histogram ,  titles , etc 

0     10     15     20     25     30     35            Hours spent studying

14 12 10 8 6 4 2

14 12 10 8 6 4 2

under 15 under 20 under 25 under 30 under 35

Hours Studying

Cumulative 

f

19 26 29 30 7

Graph… Graph…

35 30 25 20 15 10 5

Pie

200 runners were asked to indicate their

favourite type of running shoe

Type Type Nike      92

Pie

3­D

2 ­ 47

Bar

Use bar charts also              

         when the order   

       in which  qualitative data are  presented      is  meaningful.       

Use bar charts also                         when the order    

       in which  qualitative data are  presented       is  meaningful.        

How could we chart this data?

Bar

Employment  Rate

Employment Rate in Canadian Cities

Employment  Rate

W in

ni pe g

Ed m

on to n

the StatCan data?

Clus tered  Bar

Comparison of Internet Use in 2000 and 2001 Comparison of Internet Use in 2000 and 2001

% of enterprises that use the Internet 2000 % of enterprises that use the Internet 2001

% of enterprises with a Web site 2000

% of enterprises with a Web site 2001

Full­Time University Faculty By Gender, Canada and Jurisdictions, 1987­88 and 1997­98

Stack ed  Bar

Canadian Full Time University Faculty

0 20 40 60 80 100 120

Full Professor Associate Professor 1987­88 1997­98 1987­88 1997­98 1987­88      1997­98   

Other  1987­88 1997­98

% Male

% Female 17

83 25 75 93 7 13 87 17 83 28 72 32 68 44 56

Make sure that your  charts              are  not      

overly cluttered

Make sure that your  charts               are  not      

overly cluttered

Population distributions are often bell shaped.               Drawing a histogram             helps verify the shape 

2 ­ 62 Line

Time Plot Time Plot

Line

O S A J J M A M F J D

N O S A J J M A M F J

D N O S A J J M A M F J

8.5 7.5 6.5

Employment Rate in Canadian Cities

52 54 56 58 60 62 64 66 68 70

W in

ni pe g

Ed m

on to n

Va nc

ou ve r

Vi ct

or ia

Line

Preparing a Line Chart for this type of data is not overly useful!

Employment Rate in Canadian Cities

52 54 56 58 60 62 64 66 68 70

W in

ni pe g

Ed m

on to n

5040

3020

100

3020

100

searchable glossary access to Statistics Canada’s  E­Stat data

…and much more!

This completes Chapter 2