Ch21 22 data analysis and interpretation

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  • 1. Quantitative Methods - Business Mathematics Data Analysis and Interpretation
  • 2. CONTENT
    • Basic Concepts
    • Frequency Distribution
      • Ungrouped and Grouped Data
      • Relative Frequency
      • Cumulative Frequency
    • Graphical Depiction of Data
      • Histogram
      • Frequency Polygon
      • Ogive
      • Pie Charts
      • Pareto Chart
  • 3. Basic Concepts
    • Population: Collection of persons / objects / items of interest (e.g. Female in India)
    • Census: Using data from whole population for a given measurement of interest (e.g. % of educated female in India)
    • Sample: A portion of population (if properly taken, representative of the population) (e.g. 50,000 females selected from various states and various age group)
    • Parameter: A descriptive measure of population, e.g. Mean income of population
    • Statistic: A descriptive measure of sample, e.g. Mean income of a sample
    • Inferential Statistics: From sample data, conclusion is drawn about population. (e.g. mean income of population is Rs. 25,000 inferred from mean income of sample
  • 4. Frequency Distribution
      • Ungrouped Data – Raw data (see Table 2.1 of BLACK)
    • Grouped Data – Data organized in Frequency Distribution (see Table 2.2 of BLACK)
    • Range: Largest No – Smallest No =12.5-1.2 = 11.3
    • Class Interval – (e.g. 3-Under 5)
      • Class Beginning Point: 3
      • Class Width: 2
      • Class Midpoint = 3+ ½*2 = 4
    • Frequency - # of observations in that class interval
    • Relative Frequency – Proportion of total frequency (i.e. Individual Class Frequency / Total Class Frequency
    • Cumulative Frequency – Running Freq. till this class
  • 5. Data Visualization: Descriptive Charts and Graphs
    • Ungrouped data: Raw data, or data that have not been summarized in any way.
    • Frequency distribution: A summary of data presented in the form of class intervals and class frequencies.
    • Grouped data: Data that have been organized into a frequency distribution .
    Sep 18, 2011
  • 6. Frequency Distribution
    • Steps in the construction of a frequency distribution
        • Determine the range of the raw data.
        • Determine how many classes a frequency distribution should have.
        • Determine the width of the class interval.
    Sep 18, 2011
  • 7. Frequency Distribution – Key Terms
    • Class Midpoint: It is the average of the two class endpoints. This value is important, because it becomes the representative value for each class in most group statistics calculations .
    • Relative Frequency: The proportion of the total frequencies that fall into any given class interval in a frequency distribution.
    • Cumulative Frequency: A running total of frequencies through the classes of a frequency distribution.
    Sep 18, 2011
  • 8. Problems
    • Do Problem 1 Chapter 2 BLACK to calculate Frequency distribution, relative frequency, cumulative frequency, etc.
  • 9. Graphical Depiction of Data
    • Histogram: It is a type of vertical bar chart constructed by graphing line segments for the frequencies of classes across the class intervals and connecting each to the X-axis to form a series of rectangles.
    • Frequency Polygon: A graph constructed by plotting a dot for the frequencies at the class midpoints and connecting the dots.
    Sep 18, 2011
  • 10. Graphical Depiction of Data
    • Ogives: An ogive is a cumulative frequency polygon; plotted by graphing a dot at each class endpoint for the cumulative or de-cumulative frequency value and connecting the dots.
    Sep 18, 2011
  • 11. Graphical Depiction of Data Sep 18, 2011
  • 12. Problems
    • Do Problem 2 Chapter 2 BLACK to draw histogram, frequency polygon, Ogive
    • Do problem 3 Chapter 2 BLACK to draw pie chart
    • Do problem 4 Chapter 2 BLACK Stem and Leaf Chart
    • Do problem 5 Chapter 2 BLACK Pareto Chart
    • Advantages of Stem and Leaf Chart
      • Raw data preserved (In frequency distribution, it is not preserved)
      • Easy to see distribution on left and right
    • Advantages of Pareto Principle
      • ABC analysis to concentrate on important aspects
    • Do Problem 6 Chapter 2 BLACK Scatter Chart