Business Statistics **** Management Information Systems
Business Statistics
Third level
First mid-term: 1436-1437
Instructor: Dr. ZRELLI Houyem
Majmaah University *****
Faculty of Science and Humanities in Ghat
Business Statistics **** Management Information Systems
Chapter 2;
Describing Data:
Frequency Tables, Frequency
Distributions, and Graphic
Presentation
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Business Statistics **** Management Information Systems
Data Presentation
Data
Presentation
Qualitative
Data
Quantitative
Data
Discrete
Variables
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Continues
Variables
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Business Statistics **** Management Information Systems
 Describing Qualitative Data
• Qualitative Data are nonnumerical
– Major Discipline
– Political Party
– Gender
– Eye color
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Business Statistics **** Management Information Systems
 Describing Qualitative Data
• Summarized in two ways:
– Class Frequency
– Class Relative Frequency
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Business Statistics **** Management Information Systems
 Describing Qualitative Data
• Class Frequency
– A class is one of the categories into which
qualitative data can be classified
– Class frequency is the number of observations in
the data set that fall into a particular class
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Business Statistics **** Management Information Systems
 Describing Qualitative Data
Example: Student evaluations
Student
Evaluation
Student
Evaluation
1
Very Good
12
Very Good
2
Good
13
Good
3
Good
14
Very Good
4
Excellent
15
Good
5
Very Good
16
Good
6
Excellent
17
Good
7
Excellent
18
Excellent
8
Good
19
Very Good
9
Excellent
20
Good
10
Good
21
Good
11
Excellent
22
Excellent
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Business Statistics **** Management Information Systems
 Describing Qualitative Data
Example: Student evaluations
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Evaluation
Frequency
Good
10
Very Good
5
Excellent
7
Total
22
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 Describing Qualitative Data
• Class Relative Frequency
– Class frequency divided by the total number of
observations in the data set
class frequency
class relative frequency =
n
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Business Statistics **** Management Information Systems
 Describing Qualitative Data
• Class Percentage
– Class relative frequency multiplied by 100
class percentage = (class relative frequency) 100
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Business Statistics **** Management Information Systems
 Describing Qualitative Data
Example: Student evaluations
Evaluation
Class
Percentage
Good
Relative
Frequency
10/22 = .455
Very Good
5/22 = .227
22.7%
Excellent
7/22 = .318
31.8%
Total
22/22 = 1.00
100%
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45.5%
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Business Statistics **** Management Information Systems
 Describing Qualitative Data
Example: Student evaluations
10
8
6
4
2
0
Good
Very Good
Excellent
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.
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Business Statistics **** Management Information Systems
 Describing Qualitative Data
Example: Student evaluations
Excellent
114.48
Good
163.8
Very Good
81.72
Pie Chart: The categories (classes) of the qualitative variable are represented by slices of a
pie. The size of each slice is proportional to the class relative frequency.
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Business Statistics **** Management Information Systems
 Describing Qualitative Data
Example: Student evaluations
Good
Very Good
Excellent
Pareto Diagram: A bar graph with the categories (classes) of the qualitative variable (i.e.,
the bars) arranged in height in descending order from left to right.
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Business Statistics **** Management Information Systems
 Quantitative data: Discrete Variable
A discrete variable can have only countable
number of values
Examples:
Family size (x = 0, 1, 2, 3, … )
Number of patients (x = 0, 1, 2, 3, … )
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Business Statistics **** Management Information Systems
 Quantitative data: Discrete Variable
Example:
The following data represent the number of children of
16 Saudi women:
3, 5, 2, 4, 0, 1, 3, 5, 2, 3, 2, 3, 3, 2, 4, 1
- Variable = X = no. of children (discrete, quantitative)
- Sample size = n = 16
- The possible values of the variable are: 0, 1, 2, 3, 4, 5
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 Quantitative data: Discrete Variable
Simple frequency distribution of the no. of children
no. of children
(variable)
0
Frequency
(no. of women)
1
1
2
0.125
12.5%
2
4
0.25
25%
3
5
0.3125
31.25%
4
2
0.125
12.5%
5
2
0.125
12.5%
1.00
100%
Total
n=16
Relative Freq. (R.F.)
(=Freq /n)
0.0625
Percentage Freq.
(= R.F. * 100%)
6.25%
Note
Total of the frequencies = n ezis elpmas e =
·Relative frequency = frequency/n
Percentage frequency = Relative frequency *100%
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Graphical representation of discrete variables
The most common form of graphs for discrete
variables is the bar chart.
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Graphical representation of discrete variables
·
Frequency bar chart
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Business Statistics **** Management Information Systems
Cumulative representation of discrete variables
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No. Of
children
Frequency
Relative
frequency
Cumulative relative
frequency
0
1
0.0625
0
1
2
0.125
0.0625
2
4
0.25
0.1875
3
5
0.3125
0.4375
4
2
0.125
0.75
5
2
0.125
0.875
Total
N=10
1.00
1
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Cumulative representation of discrete variables
Cumulative distribution
Fi
.
.
.
1
0.9
0.8
0.7
0.6
.
0.5
0.4
0.3
0.2
0.1
.
. .
0
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2
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3
4
5
modalities
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 Quantitative data: Continuous variables
A continuous variable can have any value
within a certain interval of values.
Examples: - height (140 < x < 190)
- blood sugar level (10 < x < 15)
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Graphical representation of continuous variables
A continuous frequency distribution CANNOT
be represented by a bar chart. It is most
appropriately represented by a histogram
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Business Statistics **** Management Information Systems
Example: Hudson Auto Repair
The manager of Hudson Auto
would like to have a better
understanding of the cost
of parts used in the engine
tune-ups performed in the
shop. She examines 50
customer invoices for tune-ups. The costs of parts,
rounded to the nearest dollar, are listed on the next
slide.
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Business Statistics **** Management Information Systems
Example: Hudson Auto Repair

Sample of Parts Cost for 50 Tune-ups
91
71
104
85
62
78
69
74
97
82
93
72
62
88
98
57
89
68
68
101
75
66
97
83
79
52
75
105
68
105
99
79
77
71
79
80
75
65
69
69
97
72
80
67
62
62
76
109
74
73
Including a line in the table for every possible
cost is not a good idea.
Need to categorize.
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Business Statistics **** Management Information Systems
Frequency Distribution
• Guidelines for Selecting Number of Classes
• Use between 5 and 20 classes.
• Data sets with a larger number of elements
usually require a larger number of classes.
•
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Smaller data sets usually require fewer classes
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Frequency Distribution
• Guidelines for Selecting Width of Classes
•Use classes of equal width.
•Approximate Class Width =
Largest Data Value  Smallest Data Value
Number of Classes
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Business Statistics **** Management Information Systems
Frequency Distribution
For Hudson Auto Repair, if we choose six classes:
Approximate Class Width = (109 - 52)/6 = 9.5  10
Parts Cost ($)Frequency
[50-60[
2
[60-70[
13
[70-80[
16
[80-90[
7
[90-100[
7
[100-110[
5
Total
50
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Business Statistics **** Management Information Systems
Preview cumulative frequencies here.
Relative Frequency and Percent Frequency
Distributions
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Parts
Relative
Cost ($) Frequency
[50-60[
.04
[60-70[
.26 2/50
[70-80[
.32
[80-90[
.14
[90-100[ .14
[100-110[ .10
Total 1.00
Majmaah University
Percent
Frequency
4
26
.04(100)
32
14
14
10
100
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Business Statistics **** Management Information Systems
Relative Frequency and Percent Frequency
Distributions

Insights Gained from the Percent Frequency
Distribution
• Only 4% of the parts costs are in the $50-60 class.
•
•
•
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30% of the parts costs are under $70.
The greatest percentage (32% or almost one-third)
of the parts costs are in the $70-80 class.
10% of the parts costs are $100 or more.
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Histogram
 Another common graphical presentation of quantitative
data is a histogram.
 The variable of interest is placed on the horizontal
axis.
 A rectangle is drawn above each class interval with
its height corresponding to the interval’s frequency,
relative frequency, or percent frequency.
 Unlike a bar graph, a histogram has no natural
separation between rectangles of adjacent classes.
In informal discussions bar graphs and histograms are often
equated. In this class you should be careful to keep them
straight.
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Histogram
Tune-up Parts Cost
18
16
Frequency
14
12
10
8
6
4
2
50
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70
80
90
100
Parts
110 Cost ($)
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Business Statistics **** Management Information Systems
Histogram (Common categories)
• Symmetric
– Left tail is the mirror image of the right tail
– Examples: heights and weights of people
Relative Frequency
.35
.30
.25
.20
.15
.10
.05
0
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Business Statistics **** Management Information Systems
Cumulative Distributions
Cumulative frequency distribution  shows the
number of items with values less than or equal to
the upper limit of each class..
Cumulative relative frequency distribution – shows
the proportion of items with values less than or
equal to the upper limit of each class.
Cumulative percent frequency distribution – shows
the percentage of items with values less than or
equal to the upper limit of each class.
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Business Statistics **** Management Information Systems
Cumulative Distributions
• Hudson Auto Repair
Cumulative Cumulative
Cumulative Relative
Percent
Frequency
Cost ($) Frequency
Frequency
0
2
[50-60[
4
.04
15
[60-70[
30
31 2 + 13 .30 15/50
[70-80[
62 .30(100)
.62
38
[80-90[
76
.76
45
[90-100[
90
.90
50
[100-110[
100
1.00
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Business Statistics **** Management Information Systems
Ogive

An ogive is a graph of a cumulative distribution.

The data values are shown on the horizontal axis.

Shown on the vertical axis are the:
• cumulative frequencies, or
• cumulative relative frequencies, or
• cumulative percent frequencies

The frequency (one of the above) of each class is
plotted as a point.

The plotted points are connected by straight lines.
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Business Statistics **** Management Information Systems
Ogive with Cumulative Percent Frequencies
Cumulative Percent Frequency
Tune-up Parts Cost
100
80
60
(89.5, 76)
40
20
Parts
Cost ($)
50
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70
80
90
100
110
Dr: ZRELLI Houyem
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End of Chapter 2