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Statistics and Optimization

Statistics and Optimization. Dr. Asawer A. Alwasiti. Contenet. 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

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Statistics and Optimization

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  1. Statistics and Optimization Dr. Asawer A. Alwasiti

  2. Contenet • 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. Chapter OneIntroduction • 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:

  8. 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

  9. 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.

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