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# 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