welcome to chapter 2 mba 541
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Welcome to Chapter 2 MBA 541. B ENEDICTINE U NIVERSITY Statistics and Frequency Distributions Describing Data: Frequency Distributions and Graphic Presentation Chapter 2. Chapter Two. Please, Read Chapter Two in Lind before viewing this presentation. Statistical Techniques in - PowerPoint PPT PresentationTRANSCRIPT
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Welcome to Chapter 2 MBA 541
BENEDICTINE UNIVERSITY
• Statistics and Frequency Distributions
• Describing Data: Frequency Distributions and Graphic Presentation
• Chapter 2
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Chapter Two
Please, Read Chapter Two
in Lind before viewing this presentation.
StatisticalTechniques in
Business &Economics
Lind
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GoalsWhen you have completed this chapter, you
will be able to:
• ONE– Organize data into a frequency distribution.
• TWO– Portray a frequency distribution in a histogram,
frequency polygon, and cumulative frequency polygon.
• THREE– Present data using such graphic techniques as
line charts, bar charts, and pie charts.
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Frequency Distribution
A Frequency Distribution is a grouping of data into
mutually exclusive categories showing the number of
observations in each class.
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Constructing a Frequency Distribution
Constructing a frequency distribution involves:
• Determining the question to be addressed
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Constructing a Frequency Distribution
Constructing a frequency distribution involves:
• Determining the question to be addressed• Collecting raw data
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Constructing a Frequency Distribution
Constructing a frequency distribution involves:
• Determining the question to be addressed• Collecting raw data• Organizing data (frequency distribution)
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Constructing a Frequency Distribution
Constructing a frequency distribution involves:
• Determining the question to be addressed• Collecting raw data• Organizing data (frequency distribution)• Presenting data (graph)
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Constructing a Frequency Distribution
Constructing a frequency distribution involves:
• Determining the question to be addressed• Collecting raw data• Organizing data (frequency distribution)• Presenting data (graph)• Drawing conclusions
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A Simple Example of Creating a Frequency Distribution
• The next few slides illustrate the steps in constructing a frequency distribution.
• As Example 1, this illustrates, clarifies, and demonstrates the conceptual steps that were just discussed.
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A Simple Example of Creating a Frequency Distribution
Background Information:
• This company employs 17 individuals.
• This company maintains employee records.
• The company wants to understand employee length of service data.
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A Simple Example of Creating a Frequency Distribution
Step 1: Determine the question to be addressed
• An employer wants to answer the question, “How many people have worked for how many years at this business?”
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A Simple Example of Creating a Frequency Distribution
Step 2: Collect the raw data.
Length of Service(in years)
4 3 2 10 6 6
5 8 4 8 4
6 2 3 3 7 5
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A Simple Example of Creating a Frequency Distribution
Step 3: Determine the class interval or width.
Here we will choose five classes with an interval of two years.
Length of Service(in years)
4 3 2 10 6 6
5 8 4 8 4
6 2 3 3 7 5
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A Simple Example of Creating a Frequency Distribution
Step 4: Tally the results into classes.
Length of Service(in years)
4 3 2 10 6 6
5 8 4 8 4
6 2 3 3 7 5
Frequency Distribution
1-2 years 2
3-4 years 6
5-6 years 57-8 years 39-10 years 1Total 17
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A Simple Example of Creating a Frequency Distribution
Step 5: Present data (graph).
Frequency Distribution of Employee Service
0
1
2
3
4
5
6
7
1-2 3-4 5-6 7-8 9-10
Years of Service
Fre
qu
en
cy
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A Simple Example of Creating a Frequency Distribution
Step 6: Draw conclusions.
Frequency Distribution
1-2 years 2
3-4 years 6
5-6 years 57-8 years 39-10 years 1Total 17
• The majority of the employees have between 3 and 6 years of service.
• Only one employee has more than 8 years of service.
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Definitions
Class Interval: The class interval is obtained by subtracting the lower limit of a class from the lower limit of the next class. The class intervals should be equal.
Class Midpoint: A point that divides a class into two equal parts. This is the average of the upper and lower class limits.
Class Frequency: The number of observations in each class.
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Example 2
Background: Dr. Tillman is Dean of the School of Business at Socastee University. He wishes to prepare a report showing the number of hours per week that students spend studying. He selects a random sample of 30 students and determines the number of hours that each student studied last week.
Hours Spent Studying Last Week
15.0 17.4 10.3 18.3 14.0 18.3
20.7 18.9 16.6 20.3 14.2 33.8
17.1 27.1 15.4 15.7 21.4 13.5
12.9 19.7 12.9 23.0 17.8 29.8
23.7 18.6 26.1 13.7 20.8 23.2
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Example 2
Step One: Decide on the number of class using the formula:
Where: k = number of classes, andn = number of observations.
•There are 30 observations so n = 30.•Two raised to the fifth power is 32.•Therefore, we should have at least 5 classes;
i.e., k = 5.
nk2
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Example 2
Step Two: Determine the class interval or width by using the formula:
Where: H = highest value, andL = lowest value.
• Round up for an interval of 5 hours.• Set the lower limit of the first class at 7.5 hours.• Generate a total of 6 classes.
H- L 33.8-10.3
i = =4.7k 5
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Example 2
Step Three: Set the individual class limits and
Steps Four and Five: Tally and count the number of items in each class.
Hours Studying Frequency, f
7.5 up to 12.5 1
12.5 up to 17.5 12
17.5 up to 22.5 10
22.5 up to 27.5 5
27.5 up to 32.5 1
32.5 up to 37.5 1
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Example 2
Hours Studying Midpoint Frequency, f
7.5 up to 12.5 10.0 1
12.5 up to 17.5 15.0 12
17.5 up to 22.5 20.0 10
22.5 up to 27.5 25.0 5
27.5 up to 32.5 30.0 1
32.5 up to 37.5 35.0 1
Class Midpoint: find the midpoint of each interval by using the following formula:
Upper Limit Lower LimitClass Midpoint
2
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Example 2 – Chart 2-11
2
3
4
5
6
78
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32333435363738
A B C D E F G H I J KHours Studying
15.0 Bin Frequency Bins Bin Frequency Midpoints23.7 10.3 1 12.5 12.5 1 10.019.7 15.0 7 17.5 17.5 12 15.015.4 19.7 11 22.5 22.5 10 20.018.3 24.4 7 27.5 27.5 5 25.023.0 29.1 2 32.5 32.5 1 30.014.2 More 2 37.5 37.5 1 35.020.8 More 013.520.717.418.612.920.313.721.418.329.817.118.910.326.115.714.017.833.823.212.927.116.6
Histogram for Hours Spent Studying
0
5
10
15
10.0 15.0 20.0 25.0 30.0 35.0
Hours Spent Studying
Frequency
Line Graph for Hours Spent Studying
0
5
10
15
10.0 15.0 20.0 25.0 30.0 35.0
Hours Spent Studying
Frequency
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Example 2
Hours Studying Midpoint Frequency, f RelativeFrequency
7.5 up to 12.5 10.0 1 1/30 = 0.0333
12.5 up to 17.5 15.0 12 12/30 = 0.4000
17.5 up to 22.5 20.0 10 10/30 = 0.3333
22.5 up to 27.5 25.0 5 5/60 = 0.1667
27.5 up to 32.5 30.0 1 1/30 = 0.0333
32.5 up to 37.5 35.0 1 1/30 = 0.0333
Total 35.0 30 30/30 = 1.0000
A Relative Frequency Distribution shows the percent of observations in each class.
Class FrequencyRelative Frequency
Total Number of Observations
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Graphic Presentations of a Frequency Distribution
A Histogram is a graph on which the class midpoints or limits are marked on the horizontal axis and the class frequencies on the vertical axis.
The class frequencies are represented by the heights of the bars and the bars are drawn adjacent to each other.
The three commonly used graphic forms are Histograms, Frequency Polygons, and
Cumulative Frequency Polygons.
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Histogram For Hours Spent Studying
0
2
4
6
8
10
12
14
10 15 20 25 30 35
Hours spent studying
Fre
qu
ency
midpoint
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Graphic Presentations of a Frequency Distribution
A Frequency Polygon consists of line segments connecting the points formed by the class midpoints and the class frequency.
The three commonly used graphic forms are Histograms, Frequency Polygons, and
Cumulative Frequency Polygons.
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Frequency Polygon For Hours Spent Studying
Line Graph for Hours Spent Studying
0
5
10
15
10.0 15.0 20.0 25.0 30.0 35.0
Hours Spent Studying
Freq
uenc
y
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Graphic Presentations of a Frequency Distribution
A Cumulative Frequency Polygon is used to determine how many or what proportion of the data values are below or above a certain value.
To create a cumulative frequency polygon, scale the upper limit of each class along the X-axis and the corresponding cumulative frequencies along the Y-axis.
The three commonly used graphic forms are Histograms, Frequency Polygons, and Cumulative Frequency Polygons.
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Cumulative Frequency TableFor Hours Spent Studying
Hours Studying Upper Limit
Frequency CumulativeFrequency
7.5 up to 12.5 12.5 1 1
12.5 up to 17.5 17.5 12 1+12 = 13
17.5 up to 22.5 22.5 10 13+10 = 23
22.5 up to 27.5 27.5 5 23+5 = 28
27.5 up to 32.5 32.5 1 28+1 = 29
32.5 up to 37.5 37.5 1 29+1 = 30
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Cumulative Frequency Polygon
For Hours Spent Studying
0
5
10
15
20
25
30
35
10 15 20 25 30 35
Hours Spent Studying
Frequency
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Line GraphsLine graphs are typically used to show the change
or trend in a variable over time.Year Males Females
1992 30.5 32.9
1993 30.8 33.2
1994 31.1 33.5
1995 31.4 33.8
1996 31.6 34.0
1997 31.9 34.3
1998 32.2 34.6
1999 32.5 34.9
2000 32.8 35.2
2001 33.2 35.5
2002 33.5 35.8
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Example 3 - Line Graphs
US Median Age by Gender
2728293031323334353637
Year
Ag
e Males
Female
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Example 3 – Chart 2-2
1234567891011121314151617181920
A B C D E F G H I J KYear Males Females1992 30.5 32.91993 30.8 33.21994 31.1 33.51995 31.4 33.81996 31.6 34.01997 31.9 34.31998 32.2 34.61999 32.5 34.92000 32.8 35.22001 33.2 35.52002 33.5 35.8
US Median Age by Gender
2728293031323334353637
Year
Ag
e Males
Female
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Bar Chart
A Bar Chart can be used to depict any of the levels of measurement: nominal, ordinal, interval or ratio.
City Number of unemployedper 100,000 population
Atlanta, GA 7300
Boston, MA 5400
Chicago, IL 6700
Los Angeles, CA 8900
New York, NY 8200
Washington, DC 8900
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Bar Chart For the Unemployment Data
Number of unemployed per 100,000 population
01,0002,0003,0004,0005,0006,0007,0008,0009,000
10,000
Cities
Num
ber
of
unem
plo
yed p
er
100,0
00 p
opula
tion
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Example 4 – Chart 2-3
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3
4
5
6
7
8
9
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A B C D E F G H I J
City Number of unemployed per 100,000 population
Atlanta, GA 7300
Boston, MA 5400
Chicago, IL 6700
Los Angeles, CA
8900
New York, NY 8200
Washington, D.C.
8900
Number of unemployed per 100,000 population
0100020003000400050006000700080009000
10000
Atlant
a, G
A
Bosto
n, M
A
Chica
go, I
L
Los Ang
eles
, CA
New Y
ork,
NY
Was
hing
ton,
D.C
.
Cities
Nu
mb
er
of
un
em
plo
yed
per
10
0,0
00
pop
ula
tion
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Pie ChartA Pie Chart is useful for displaying a relative frequency distribution. A circle is divided proportionally to the relative frequency and portions of the circle are allocated for the different groups.A sample of 200 runners were asked to indicate their favorite type of running shoe.Draw a pie chart based on the following information.
Type of shoe # of runners % of total
Nike 92 46.0
Adidas 49 24.5
Reebok 37 18.5
Asics 13 6.5
Other 9 4.5
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Pie Chart For Running Shoes
Pie Chart for running shoes
46.0%
24.5%
18.5%
6.5%
4.5%
Nike
AdidasReebok
AsicsOther
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Example 5 – Chart 2-4
1
2
3
4
5
678910111213141516
A B C D E F G H I
Type of shoe
# of runners
Nike 92Adidas 49Reebok 37Asics 13Other 9
Pie Chart for running shoes
46.0%
24.5%
18.5%
6.5%
4.5%
Nike
Adidas
Reebok
Asics
Other