walpole, r. e., myers, r. h., and s. l. myers saddle river
TRANSCRIPT
![Page 1: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/1.jpg)
![Page 2: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/2.jpg)
Walpole, R. E., Myers, R. H., and S. L. Myers
(2007), Probability and Statistics for Engineers and
Scientists, 8th ed., Prentice-Hall, Inc., Upper
Saddle River, New Jersey.
![Page 3: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/3.jpg)
سلطان، خلف.د هندي، محمود.د
، الإحصائي التحليل لطرق مفاهيم
.2004الرشد مكتبة
![Page 4: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/4.jpg)
The first lecture
We will examine in this lecture :
•Definition of Statistics.
•The difference between the population and
the sample.
•Branches of Statistics.
•Displaying data.
![Page 5: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/5.jpg)
Introduction to Statistics
The reasons for the appearance of Statistics:
• Census community.
• Inventory of the wealth of individuals.
• Data on births, deaths and production and
consumption.
![Page 11: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/11.jpg)
Definition statistics
Statistics is a science of collecting ,
organizing , analyzing and interpreting
data in order to make decisions.
![Page 13: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/13.jpg)
Definition of a population
A population is the collection of all
outcomes, responses, measurements, or
counts that are of interest.
![Page 14: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/14.jpg)
• The number of students in computer science college.
• The number of cards in a deck.
Finite population: the total number of its
observations is a finite number.
Infinite population: the total number of its
observations is an infinite number.
Types of a population
• The number of stars in sky.
• The observations obtained by measuring the atmospheric
pressure every day from the past on into the future .
![Page 15: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/15.jpg)
Definition of a sample
A sample is a subset of a population that
is representative of the population.
![Page 16: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/16.jpg)
•We can not study the population :huge,
destinations.
•Preservation from loss
•Less cost.
•Save time.
•More inclusive.
•More accuracy.
Reasons draw a sample, rather
than study a population
![Page 17: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/17.jpg)
Branches of Statistics
Descriptive statistics is the branch of statistics
that involves the organization, summarization ,
and display of data.
Statistical inference is the branch of statistics that
involves using a sample to draw conclusions about a
population.
![Page 18: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/18.jpg)
Definition of data
Data consist of information coming from
observations, counts, measurement, or
responses. The singular for data is datum.
1. Quantitative data: it can be measured in the
usual sense like length, weight , and age.
Types of data
2. Qualitative data: it cannot be measured in the
usual sense but it can be ordered or ranked. for
example:marital status,blood group and eye color
![Page 20: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/20.jpg)
67 90 74 71 90 73 74 70 95 51
69 85 84 72 80 50 89 83 72 91
79 78 75 87 76 91 76 87 82 62
70 86 57 73 82 64 88 81 96 71
91 77 66 83 90 74 85 75 81 80
Frequency Class
Intervals
3 50-59
5 60-69
18 70-79
16 80-89
8 90-99
50 Total
![Page 21: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/21.jpg)
Organization Data
We will learn how to creat:
•Frequency table.
•Relative frequency table.
•Percentage frequency table.
![Page 22: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/22.jpg)
Example (1):
the following data represent the level
of 60 students in a course:
D B E C D B D C E A
B E C D B D D A E C
C D A C E D C C D B
D E D D A D D C D C
D A B D B D C D C E
D B C C E D C C D A
![Page 23: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/23.jpg)
67 90 74 71 90 73 74 70 95 51
69 85 84 72 80 50 89 83 72 91
79 78 75 87 76 91 76 87 82 62
70 86 57 73 82 64 88 81 96 71
91 77 66 83 90 74 85 75 81 80
Example (2):
the following data represent the
marks of 50 students in a course:
![Page 24: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/24.jpg)
Definition of frequency table
(frequency distribution)
A frequency distribution is a table that shows
classes or intervals of data entries with a
count of the number of entries in each class.
The frequency f of a class is a number of
data entries in the class.
![Page 25: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/25.jpg)
Organization qualitative data
![Page 26: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/26.jpg)
Example (1):
the following data represent the level
of 60 students in a course:
D B E C D B D C E A
B E C D B D D A E C
C D A C E D C C D B
D E D D A D D C D C
D A B D B D C D C E
D B C C E D C C D A
![Page 27: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/27.jpg)
frequency tally Level
A
B
C
D
E
Total
![Page 28: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/28.jpg)
Example (1):
the following data represent the level
of 60 students in a course:
D B E C D B D C E A
B E C D B D D A E C
C D A C E D C C D B
D E D D A D D C D C
D A B D B D C D C E
D B C C E D C C D A
![Page 29: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/29.jpg)
frequency tally Level
6 ││││ │ A
B
C
D
E
Total
![Page 30: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/30.jpg)
Example (1):
the following data represent the level
of 60 students in a course:
D B E C D B D C E A
B E C D B D D A E C
C D A C E D C C D B
D E D D A D D C D C
D A B D B D C D C E
D B C C E D C C D A
![Page 31: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/31.jpg)
frequency tally Level
6 ││││ │ A
8 ││││ │ │ │ B
C
D
E
Total
![Page 32: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/32.jpg)
frequency tally Level
6 ││││ │ A
8 ││││ │ │ │ B
16 ││││ ││││ ││││ │ C
22 ││││ ││││ ││││ │ │ D
8 ││││ │ │ │ E
60 Total
![Page 33: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/33.jpg)
Table(1): frequency table
frequency Level
6 A
8 B
16 C
22 D
8 E
60 Total
![Page 34: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/34.jpg)
Table(1): frequency table
Total E D C B A Level
60 8 22 16 8 6 frequency
![Page 35: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/35.jpg)
Organization quantitative data
![Page 36: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/36.jpg)
Example (2):
the following data represent the marks
of 50 students in a course:
67 90 74 71 90 73 74 70 95 51
69 85 84 72 80 50 89 83 72 91
79 78 75 87 76 91 76 87 82 62
70 86 57 73 82 64 88 81 96 71
91 77 66 83 90 74 85 75 81 80
![Page 37: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/37.jpg)
Frequency distribution for
quantitative data
For large samples, we can’t use the simple
frequency table to represent the data.
We need to divide the data into groups or intervals
or classes.
So, we need to determine:
•First step :the number of intervals (k).
•Second step :the range (R).
•Third step :the Width of the interval (w).
![Page 38: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/38.jpg)
The number of intervals (k)
A small number of intervals are not good because
information will be lost.
A large number of intervals are not helpful to
summarize the data.
A commonly followed rule is that 5 k 20 or the
following formula may be used, k=1+3.322 (log n).
We select 5 intervals in our example.
![Page 39: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/39.jpg)
The range (R)
It is the difference between the maximum and the
minimum observation (entries) in the data set.
R = the maximum entry - the minimum entry
R =96-50
=46
![Page 40: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/40.jpg)
Example (2):
the following data represent the marks of
50 students in a course:
67 90 74 71 90 73 74 70 95 51
69 85 84 72 80 50 89 83 72 91
79 78 75 87 76 91 76 87 82 62
70 86 57 73 82 64 88 81 96 71
91 77 66 83 90 74 85 75 81 80
![Page 41: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/41.jpg)
The range (R)
It is the difference between the maximum and the
minimum observation(entries) in the data set.
R =Xmax- Xmin
R =96-50
=46
![Page 42: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/42.jpg)
The Width of the interval (w)
469.4 10
5w
Class intervals generally should be of the same
width. Thus, if we want k intervals, then w is chosen
such that w R/k.
![Page 43: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/43.jpg)
Forth step:
Choose the minimum observation to be the lower limit of the
first interval and add the width of interval to get the lower
limit of the second interval and so on
the lower limit of the second interval
50+10=60
the lower limit of the third interval
60+10=70 the lower limit of the fourth interval
70+10=80
the lower limit of the fifth interval
80+10=90
![Page 44: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/44.jpg)
Fifth step:
To find the upper limit of any interval add the following to the lower limit
of interval :
W-1=10-1
=9
the upper limit of second interval
60+9=69 the upper limit of third interval
70+9=79
the upper limit of fourth interval
80+9=89
the upper limit of first interval
50+9=59
the upper limit of fifth interval
90+9=99
![Page 45: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/45.jpg)
frequency tally Class
interval
50-59
60-69
70-79
80-89
90-99
Total
![Page 46: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/46.jpg)
Example (2):
the following data represent the marks
of 50 students in a course:
67 90 74 71 90 73 74 70 95 51
69 85 84 72 80 50 89 83 72 91
79 78 75 87 76 91 76 87 82 62
70 86 57 73 82 64 88 81 96 71
91 77 66 83 90 74 85 75 81 80
![Page 47: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/47.jpg)
frequency tally Class
interval
3 │││ 50-59
60-69
70-79
80-89
90-99
Total
![Page 48: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/48.jpg)
67 90 74 71 90 73 74 70 95 51
69 85 84 72 80 50 89 83 72 91
79 78 75 87 76 91 76 87 82 62
70 86 57 73 82 64 88 81 96 71
91 77 66 83 90 74 85 75 81 80
Example (2):
the following data represent the
marks of 50 students in a course:
![Page 49: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/49.jpg)
frequency tally Class
interval
3 │││ 50-59
5 ││││ 60-69
18 ││││ ││││ ││││ │ │ │
70-79
16 ││││ ││││ ││││ ││
80-89
8 ││││ │ │ │ 90-99
50 Total
![Page 50: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/50.jpg)
Table(2): frequency table of students’
marks
frequency Class
interval
3 50-59
5 60-69
18 70-79
16 80-89
8 90-99
50 Total
![Page 51: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/51.jpg)
Table(2): frequency table of
students’ marks
Total 90-99 80-89 70-79 60-69 50-59
Cla
ss
inte
rva
l
50 8 16 18 5 3
fre
qu
en
cy
![Page 52: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/52.jpg)
Definition of the true class
intervals
the true lower unit = the lower limit - 0.5
the true upper unit = the upper limit + 0.5
![Page 53: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/53.jpg)
frequency True class interval Class
interval
3 50-59
5 60-69
18 70-79
16 80-89
8 90-99
50 Total
49.5-59.5
59.5-69.5
69.5-79.5
79.5-89.5
89.5-99.5
![Page 54: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/54.jpg)
Definition of the Mid-interval
(Midpoints)
the Mid-interval(Midpoints)
=(the lower limit+ the upper limit)/2
![Page 55: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/55.jpg)
frequency Midpoints True class interval
3 49.5-59.5
5 59.5-69.5
18 69.5-79.5
16 79.5-89.5
8 89.5-99.5
50 Total
2
5.495.59
2
5.595.69
54.5
64.5
74.5
84.5
94.5
![Page 56: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/56.jpg)
the relative frequency of interval=the
frequency of interval/the sum of
frequencies (n)
Definition of the relative frequency
![Page 57: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/57.jpg)
the relative frequency table
the relative
frequency frequency
Class
interval
3 50-59
5 60-69
18 70-79
16 80-89
8 90-99
50 Total
50
3
1
50
50.06
0.10
0.36
0.32
0.16
![Page 58: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/58.jpg)
the percentage frequency = the relative
frequency 100
Definition of the percentage
frequency
![Page 59: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/59.jpg)
the percentage frequency
table the percentage
frequency the relative
frequency Class
interval
0.06 50-59
0.10 60-69
0.36 70-79
0.32 80-89
0.16 90-99
1 Total 100
0.06×100
0.10×100
6
10
36
32
16
![Page 60: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/60.jpg)
the
percentage
frequency
the
relative
frequency frequency Midpoints True class interval
Class
interval
6 0.06 3 54.5 49.5-59.5 50-59
10 0.10 5 64.5 59.5-69.5 60-69
36 0.36 18 74.5 69.5-79.5 70-79
32 0.32 16 84.5 79.5-89.5 80-89
16 0.16 8 94.5 89.5-99.5 90-99
100 1 50 Total
![Page 61: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/61.jpg)
Example
Find from the tabe:
• The Width of the interval
• The midpoints
• True class intervals
• The relative frequency of
intervals.
• The percentage frequency of
intervals.
frequency Class
interval
100 16-20
122 21-25
900 26-30
207 31-35
795 36-40
568 41-45
322 46-50
![Page 62: Walpole, R. E., Myers, R. H., and S. L. Myers Saddle River](https://reader030.vdocument.in/reader030/viewer/2022012123/61dddf3433f07806f90346a9/html5/thumbnails/62.jpg)
Summary of lecture
In these lecture we
create:
•frequency table
•the percentage frequency
table
•the relative frequency table