Statistics and optimization

1. Dr. Asawer A. Alwasiti

2.  Chapter one: Introduction
 Chapter two: Frequency Distribution
 Chapter Three: Measures of Central Tendency
 Chapter Four: Measures of Dispersion
 Chapter Five: The Polynomial Distribution
 Chapter Six: Curve Fitting
 Chapter Seven: Correlation Theory

3.  Statistics: is concerned with scientific methods for
collecting, organizing, summarizing, presenting and
analyzing data as well as drawing valid conclusions and
making reasonable decisions.
 Types of data:
 Quantitative data : are those that represent the quantity or
amount of something, measured on a numerical scales.
For example; the power frequency
 Qualitative data: it’s the data that can only classified i.e.
posses no numerical representation
 Population: refers to all the persons, objects, source or
measurements under consideration, or it is a data set that
is our target of interest.
 Sample: refers to any portion of the population

4.  Descriptive Statistics: used to organize, summarize and
describe measures of sample. It uses numbers to
summarize information which is known about some
situation.
 Inductive (inference) statistics: are used to predict
population parameters from sample measures.
 Variables: is a symbol such as X, Y ,H…. which can assume
any of the prescribed set of values. It contains qualitative
and quantitative variables
 Continuous variable: can theoretically assume any value
between two given values depending on accuracy of
measurements
 Discrete variable: all data can be obtained from counting
 Parameter: the measures which describe population
characteristics.


5.  Example:
 The reliability of computer system is measured in
terms of life length of a specific hardware
component (e.g hard disk life). To estimate the
reliability of a particular system , 100 computer
component are tested until they fail, under their
life length are recorded.
 What is the population of interest?
 What is the sample?
 Are the data are qualitative or quantitative?
 How could the sample information be used to
estimate the reliability of the computer system?


6.  Qualitative Data
They are usually achieved using Bar graph or Pie chart
 Bar graph: the category (class) of the qualitative variable is
represented by Bar graph in which the height of each bar is
either the class frequency, class relative frequency or class
percentage.
 Pie chart: the category (class) of the quantitative variable is
represented by Pie chart. The size of each slice is proportional to
the class relative frequency.
 Pareto diagram: a bar graph with the category (class) of the
qualitative variable arranged by height in descending order from
left to right.

7.  Example:
 Group of researchers investigating the safety of nuclear
power reactors and the hazard of using energy, they
discovered 45 energy related accident worldwide since1977
that resulted in multi factories as:
category frequency
Coal mine collapse 7
Dam frailer 4
Gas explosion 28
lightning 1
Nuclear reactor 1
Oil fire 4
total 45

8. Chart of Causes
Coal mine collapse
Dam frailer
Gas explosion
lightning
Nuclear reactor
Oil fire
Causes
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Frequency
Pie Chart of Causes
Coal mine collapse
Dam frailer
Oil fire
Nuclear reactor
lightning
Gas explosion

9.  Quantitative Data
 It can be represented in graphical or numerical way
 Graphical representation
Quantitative Data can be represented graphically by Histogram
 Frequency distribution
 Raw data: are collected data which have been collected numerically
 Array: arranged of raw data in ascending or descending order.
 Range: the difference between the largest and smallest value
 Frequency distribution: a table arrangement of data by classes together with the corresponding
class frequencies.
 Class interval: A symbol defining the class.
 Class mark: is the mid point of the class interval
 Formation of frequency distribution:
 Determine the largest and smallest observation
 Take total width = range + 1 unit in the last significant digit
 Dived total width in 5-20 class of equal width
 Calculate class width, interval and class mark
 Calculate frequencies

 Histogram
 Graphical representation of frequency distribution consist of a set of rectangular having:
 Basis with centers at class marks and lengths equal to the class width
 Area proportional to class frequencies

 Frequency polygon
 Formed by connecting the mid points of the tops of the rectangular in the histogram
 Relative frequency
 Is the frequency of the class divided by the total frequency and expressed as a percentage

10.  Example
 The pH level of drilling mud of well that determined within 24 hr is shown in table
below, make the frequency distribution table and graph the data
 Example
7.25 7.26 7.36 7.36 7.34 7.3
7.37 7.3 7.35 7.26 7.34 7.29
7.33 7.39 7.34 7.39 7.39 7.28
7.38 7.31 7.32 7.35 7.3 7.29
7.3 7.39 7.24 7.33 7.37 7.32
7.35 7.34 7.35 7.3 7.25 7.36
7.34 7.34 7.37 7.34 7.33 7.32
7.38 7.32 7.35 7.39 7.33 7.38
7.41 7.42 7.45 7.4 7.41 7.43
7.39 7.43 7.46 7.4 7.4 7.45
 The viscosity of 40 sample of drilling mud measured in cp is shown below.
 Represent them in frequency table and with histogram.
50.2 49.3 49.9 50.1 50.5 49
51.1 49.7 50.3 49.9 51.4 49.5
49.8 49.6 49.5 49.8 50.7 51.3
50.2 50.4 50 50.7 48.6 50.8
48.9 50 50 50.3 49.4 50.2
49.9 48.6 50 49.4 50.6 50.3
50 49.9 50.6 50.8