Statistics (Stat 101)
Sameh Saadeldin Ahmed
Associate Professor of Environmental Eng.
Civil Engineering Department
Engineering College
Almajma’ah University
smohamed1@ksu.edu.sa
http://faculty.ksu.edu.sa/SaMeH
Stat 101
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Chapter 1
Week
1st
week
Stat 101
Subject
Content
Concepts of •What is Statistics?
Probability •Types of Statistics
and Statistics
•Basic Terms
•Types of Variables
•Sources of Data
•Data Collection
Approaches
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Contents (week by week)
Week
2nd
week
3rd
week
Stat101
Subject
Content
•Organizing and Graphing
Organizing Qualitative Data
•Organizing and Graphing
Data
Quantitative Data
•Shapes of Histograms
Histogram, Polygon,
Frequency Curve
•Cumulative Frequency
Distributions
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2.1 Raw Data
Data recorded in the sequence in which they
are collected and before they are processed or
ranked are called raw data
Example 2.1:
Table 2.1 gives a quantitative raw data for the
ages of 50 students selected from a college.
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Tables 2.1 and 2.2: Age and Grades of 50 students
21 19 24 25 29 34 26 27 37 33
18 20 19 22 19 19 25 22 25 23
25 19 31 19 23 18 23 19 23 26
22 28 21 20 22 22 21 20 19 21
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C
A
B
D
C
C
D
C
C
C
A
A
C
A
A
A
D
B
D
C
C
A
D
B
B
A
C
A
D
D
B
D
C
B
B
C
C
B
A
B
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2.2 Organizing and Graphing
Qualitative Data
• Data sets are organized into tables, and data
are displayed using graphs.
2.2.1 Frequency Distribution
A frequency distribution exhibits how the
frequencies are distributed over various
categories.
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Example 2.2:
Table 2.3 shows the grades of 60 students in Math
105. It is required to summarise the data in a table
form.
Tables 2.3 : Grads of 60 Students in Math 105
D B
E
C
B
E
C
D B
C
D A C
D E
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D B
E
D C
E
A
D D A E
C
D C
C
D B
D D A D D C
D C
D A B
D B
D C
D C
D B
C
D C
C
C
E
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E
D A
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Solution
Type
(grade)
Tally
A
//// /
B Type (grade)
C A
B
D
E C
SUMD
E
SUM
6
Frequency (f) 8
6
16
8
22
16
8
22
60
8
60
Category
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Frequency
(f)
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frequency
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Frequency Distribution for Qualitative Data
A frequency distribution for qualitative
data lists all categories and the number of
elements that belong to each of the category.
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2.2 Organizing and Graphing
Qualitative Data
2.2.1
Frequency Distribution
2.2.2
Relative Frequency & Percentage
A relative frequency of a category is obtained
by dividing the frequency of that category by
the sum of all frequencies.
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Calculating Relative Frequency of a Category
Relative frequency of a category = frequency of
that category / sum of all frequencies
Calculating Percentage
Percentage = (Relative frequency) x 100
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Example 2.3:
Determine the relative frequency and percentage
distributions for the data in Table 2.3
Solution:
Type Frequency
(f)
A
B
C
D
E
SUM
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6
8
16
22
8
60
Relative
Frequency
6/60 = 0.1
8/60 = 0.1333
16/60 = 0.266
22/60 = 0.366
8/60 = 0.133
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Percentage
0.1 (100) = 10
0.133 (100) = 13.3
0.266 (100) = 26.6
0.366 (100) = 36.6
0.133 (100) = 13.3
100
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Example 2.4:
The following data represents the marks of 50 students
in a subject
51 95 70 74 73 90 71 74 90 67
91 72 83 89 50 80 72 84 85 69
62 82 87 76 91 76 87 75 78 79
71 96 81 88 64 82 73 57 86 70
You are required to:
•Construct a table shows grade distribution of the student’s grades.
•A table shows the frequency distribution of the student’s marks.
•A table shows the relative distribution of the student’s marks.
•A table shows the percentage frequency distribution of the student’s
marks.
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Solution
1- A table shows the distribution of the student’s grades
Category
Tally
Frequency
50 – 59
///
3
60 – 69
5
70 – 79
18
Category
Frequency
80 – 89
16
3
90 - 99 50 – 59
8
60 – 69
5
SUM
50
70 – 79
18
90 - 99
SUM
8
50
2- A table show the Frequency distribution of the
16
student’s marks 80 – 89
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3- A table shows the relative distribution of the student’s
marks
Category Frequency (f) Relative
Frequency
50 – 59
60 – 69
70 – 79
80 – 89
90 - 99
SUM
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3
5
18
16
8
50
3/50 = 0.06
5/50 = 0.10
18/50 = 0.36
16/50 = 0.32
8/50 = 0.16
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4- A table shows the percentage frequency distribution
of the student’s marks.
Category
Frequency Relative
(f)
Frequency
Percentage
50 – 59
60 – 69
70 – 79
80 – 89
90 - 99
SUM
3
5
18
16
8
50
0.06 (100) = 6
0.10 (100) = 10
0.36 (100) = 36
0.32 (100) = 32
0.16 (100) = 16
100
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3/50 = 0.06
5/50 = 0.10
18/50 = 0.36
16/50 = 0.32
8/50 = 0.16
1.00
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2.2 Organizing and Graphing
Qualitative Data
2.2.1
Frequency Distribution
2.2.2
Relative Frequency & Percentage
2.2.3 Graphical Presentation of Qualitative
Bar Graphs
Pie Chart.
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Bar Graphs
To construct the bar graph or bar chart, we mark the
various categories on the horizontal axis (all categories
are represented by intervals of the same width). The
frequencies are presented on the vertical axis. The
height of the bar represents the frequency of the
corresponding category.
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The bar graphs for the relative frequency and
percentage distributions can be drawn by making
the relative frequencies or percentages, instead
of the class frequencies on the vertical axis.
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Pie Chart
A circle divided into portions that represent the
relative frequencies or percentages of a
population or a sample belonging to different
categories.
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2.3 Organizing and Graphing
Quantitative Data
2.3.1 Frequency Distribution
Table 2.4 gives the weekly earnings of 100 employees of a
large company. The first column lists the classes, which
represent the (quantitative) variable weekly earnings. For
quantitative data, an interval that includes all the values that
falls within two numbers. The lower and upper limits, is called
a class. Note that the classes always represent a variable. The
second column lists the number of employees who have
earnings within each class (frequency).
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Table 2.4: Weekly earnings of 100 employees of a
company
variable
Second
Class
Lower Limit
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Weekly earnings
(dollars)
401 to 600
601 to 800
801 to 1000
1001 to 1200
1201 to 1400
1401 to 1600
Number
of employees (f)
9
22
39
15
9
6
Upper Limit
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Frequency of
Third class
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Frequency Distribution for Quantitative Data
A frequency distribution for quantitative data
lists all classes and the number of values that
belong to each class. Data in the form of a
frequency distribution are called grouped data.
To find the midpoint of the upper limit of the first class and the lower
limit of the second class in Table 2.4, we divide the sum of these two
limits by 2. Thus, this midpoint is
[600 + 601] / 2 = 600.5
The value 600.5 is called the upper boundary of the first class and
the lower boundary of the second class.
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Class Boundary
The class boundary is given by the midpoint of
the upper limit of one class and the lower
limit of the next class.
We can convert the class limits of table 2.4 to class
boundaries, which are also called real class limits.
The second column of table 2.5 lists the boundaries
for table 2.4.
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Table 2.5: Class boundaries, Class widths, and Class
midpoints for Table 2.4
Class Limits
Class boundaries
401 to 600
601 to 800
801 to 1000
1001 to 1200
1201 to 1400
1401 to 1600
400.5 to less than 600.5
600.5 to less than 800.5
800.5 to less than 1000.5
1000.5 to less than 1200.5
1200.5 to less than 1400.5
1400.5 to less than 1600.5
Class
Class
width Midpoint
200
200
200
200
200
200
500.5
700.5
900.5
1100.5
1300.5
1500.5
The difference between the two boundaries of a class gives the
class width. The class width is called the class size.
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Finding Class Width
Class width = Upper boundary – Lower boundary
The class midpoint or mark is obtained by dividing the sum
of the two limits (or the two boundaries) of a class by 2.
Calculating Class Midpoint or Mark
Class midpoint or mark = [Lower limit +
Upper limit] / 2
Thus the midpoint of the first class in Table 2.4 or Table 2.5 is
calculated as follows:
Midpoint of the first class = [401 + 600] / 2 = 500.5
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Example 2.5:
Use the data given in example 2.4 to calculate the class
limits, class boundaries, midpoints and list the
calculated relative frequencies and percentage, all in
one table. A table shows all the above and the class
midpoint.
Solution:
Class
Limits
Class
Boundaries
Class
Midpoint
Frequency
f
Relative
Percentage
Frequency
50 – 59
60 – 69
70 – 79
80 – 89
90 – 99
SUM
49.5 – 59.5
59.5 – 69.5
69.5 – 79.5
79.5 – 89.5
89.5 – 99.5
54.5
64.5
74.5
84.5
94.5
3
5
18
16
8
50
0.06
0.10
0.36
0.32
0.16
1.00
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10
36
32
16
100
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End of Part 3
Get ready for a quiz (2)……
next lecture!!
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