1. STATISTICS AND OPTIMIZATION Dr. Asawer A. Alwasiti

2. Contenet  Chapter One: introduction  fundamental elements of statistics, types of data, Methods of describing data, measures of central tendency, measures of variation measures of relative standing  Chapter Two: Probability  discreet of random variable: the probability distribution, the binomial probability distribution, The hypogeometric probability distribution, Poison distribution.  Continuous random distribution: the continuous random variable, uniform probability distribution, normal probability distribution  Chapter Three: Testing of Hypothesis  Sampling distributions – Testing of hypothesis for mean, variance, proportions and differences using Normal, t, Chi- square and F distributions - Tests for independence of attributes and Goodness of fit.  Chapter Four: Simple linear regression  Regression model, methods of least squares, the coefficient of correlation, The coeffiecnt of determination  Chapter Five DESIGN OF EXPERIMENTS  Experimental design terminology, factorial design Completely randomized design – Randomized block design

3. Chapter One Introduction  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. Graphical method of representation  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: categoryfrequency Coal mine collapse7 Dam frailer4 Gas explosion28 lightning1 Nuclear reactor1 Oil fire4 total45

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  The viscosity of 40 sample of drilling mud measured in cp is shown below.  Represent them in frequency table and with histogram. 7.257.267.36 7.347.3 7.377.37.357.267.347.29 7.337.397.347.39 7.28 7.387.317.327.357.37.29 7.37.397.247.337.377.32 7.357.347.357.37.257.36 7.34 7.377.347.337.32 7.387.327.357.397.337.38 7.417.427.457.47.417.43 7.397.437.467.4 7.45 50.249.349.950.150.549 51.149.750.349.951.449.5 49.849.649.549.850.751.3 50.250.45050.748.650.8 48.950 50.349.450.2 49.948.65049.450.650.3 5049.950.650.8