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# Ch21 22 data analysis and interpretation

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### Ch21 22 data analysis and interpretation

1. 1. Quantitative Methods - Business Mathematics Data Analysis and Interpretation
2. 2. CONTENT <ul><li>Basic Concepts </li></ul><ul><li>Frequency Distribution </li></ul><ul><ul><li>Ungrouped and Grouped Data </li></ul></ul><ul><ul><li>Relative Frequency </li></ul></ul><ul><ul><li>Cumulative Frequency </li></ul></ul><ul><li>Graphical Depiction of Data </li></ul><ul><ul><li>Histogram </li></ul></ul><ul><ul><li>Frequency Polygon </li></ul></ul><ul><ul><li>Ogive </li></ul></ul><ul><ul><li>Pie Charts </li></ul></ul><ul><ul><li>Pareto Chart </li></ul></ul>
3. 3. Basic Concepts <ul><li>Population: Collection of persons / objects / items of interest (e.g. Female in India) </li></ul><ul><li>Census: Using data from whole population for a given measurement of interest (e.g. % of educated female in India) </li></ul><ul><li>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) </li></ul><ul><li>Parameter: A descriptive measure of population, e.g. Mean income of population </li></ul><ul><li>Statistic: A descriptive measure of sample, e.g. Mean income of a sample </li></ul><ul><li>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 </li></ul>
4. 4. Frequency Distribution <ul><ul><li>Ungrouped Data – Raw data (see Table 2.1 of BLACK) </li></ul></ul><ul><li>Grouped Data – Data organized in Frequency Distribution (see Table 2.2 of BLACK) </li></ul><ul><li>Range: Largest No – Smallest No =12.5-1.2 = 11.3 </li></ul><ul><li>Class Interval – (e.g. 3-Under 5) </li></ul><ul><ul><li>Class Beginning Point: 3 </li></ul></ul><ul><ul><li>Class Width: 2 </li></ul></ul><ul><ul><li>Class Midpoint = 3+ ½*2 = 4 </li></ul></ul><ul><li>Frequency - # of observations in that class interval </li></ul><ul><li>Relative Frequency – Proportion of total frequency (i.e. Individual Class Frequency / Total Class Frequency </li></ul><ul><li>Cumulative Frequency – Running Freq. till this class </li></ul>
5. 5. Data Visualization: Descriptive Charts and Graphs <ul><li>Ungrouped data: Raw data, or data that have not been summarized in any way. </li></ul><ul><li>Frequency distribution: A summary of data presented in the form of class intervals and class frequencies. </li></ul><ul><li>Grouped data: Data that have been organized into a frequency distribution . </li></ul>Sep 18, 2011
6. 6. Frequency Distribution <ul><li>Steps in the construction of a frequency distribution </li></ul><ul><ul><ul><li>Determine the range of the raw data. </li></ul></ul></ul><ul><ul><ul><li>Determine how many classes a frequency distribution should have. </li></ul></ul></ul><ul><ul><ul><li>Determine the width of the class interval. </li></ul></ul></ul>Sep 18, 2011
7. 7. Frequency Distribution – Key Terms <ul><li>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 . </li></ul><ul><li>Relative Frequency: The proportion of the total frequencies that fall into any given class interval in a frequency distribution. </li></ul><ul><li>Cumulative Frequency: A running total of frequencies through the classes of a frequency distribution. </li></ul>Sep 18, 2011
8. 8. Problems <ul><li>Do Problem 1 Chapter 2 BLACK to calculate Frequency distribution, relative frequency, cumulative frequency, etc. </li></ul>
9. 9. Graphical Depiction of Data <ul><li>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. </li></ul><ul><li>Frequency Polygon: A graph constructed by plotting a dot for the frequencies at the class midpoints and connecting the dots. </li></ul>Sep 18, 2011
10. 10. Graphical Depiction of Data <ul><li>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. </li></ul>Sep 18, 2011
11. 11. Graphical Depiction of Data Sep 18, 2011
12. 12. Problems <ul><li>Do Problem 2 Chapter 2 BLACK to draw histogram, frequency polygon, Ogive </li></ul><ul><li>Do problem 3 Chapter 2 BLACK to draw pie chart </li></ul><ul><li>Do problem 4 Chapter 2 BLACK Stem and Leaf Chart </li></ul><ul><li>Do problem 5 Chapter 2 BLACK Pareto Chart </li></ul><ul><li>Advantages of Stem and Leaf Chart </li></ul><ul><ul><li>Raw data preserved (In frequency distribution, it is not preserved) </li></ul></ul><ul><ul><li>Easy to see distribution on left and right </li></ul></ul><ul><li>Advantages of Pareto Principle </li></ul><ul><ul><li>ABC analysis to concentrate on important aspects </li></ul></ul><ul><li>Do Problem 6 Chapter 2 BLACK Scatter Chart </li></ul>