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# MGTOP 215 Chapter 2 MGTOP 215

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This 4 page Class Notes was uploaded by Megan Lester on Wednesday September 28, 2016. The Class Notes belongs to MGTOP 215 at Washington State University taught by Sung Ahn in Fall 2015. Since its upload, it has received 6 views.

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Date Created: 09/28/16

Chapter Two 1/16 - 1/26 Tuesday, January 20, 2015 12:49 PM MgtOp 215 Chapter 2 Dr. Ahn In this chapter we will study how to organize and summarize (raw) data into a meaningful way. Categorical Data A Summary Table presents tallied responses as frequencies or percentages for each category. Example 1: Refer to Table 2.3 of Example 2.1 on p.38 of the textbook which used the data set “RetirementFunds.” A Contingency Table summarizes data with two or more categories by cross-tabulating or tallying jointly. Example 2: Refer to Tables 2.3 & 2.4 on p.38 of the textbook which used the data set “RetirementFunds.” A Bar chart and a Pareto diagram are used for graphical representationfor categorical data A Pie chart is a circle divided into portions that represent the relative frequencies of categorical data. Example 3: Refer to Figure 2.1 on p. 51 of the textbook. These can be easily constructed using PHStat2: Refer to Excel Guide on p. 85. MSL Homework: 2.1, 2.9 (on pp. 40-41), 2.27 (on p. 56) HC Homework: 2.25 (on. p.56) Example 4. The following data are 227 observationsof the 1-year return % of the Growth Funds in the data file “RetirementFunds.” (Refer to p. 34 of the textbook for further detail and Appendix C on p. 729 for how to access the data.). As we cannot make sense out of the (raw) data as they are, we will “transform”the data into meaningful forms. Ordered data: data arranged in ascending order or in descending order; easy to pick out extremes, typical values, and concentration of values. To order data in MS Excel,Data > Sort… A frequency distribution(table) is a summary table in which data are arranged into conveniently established, numerically ordered class groupings or categories. The number of observationsfalling in eachclass is called the class frequency. It is a way of organizing raw data (that are considered continuous) into a meaningful way. Example 5. Refer to the data in Example 4. Construct a frequency table. Construction of the frequency table: MGTOP 215 Page 1 Construction of the frequency table: 1 Determine the range of the raw data Range = largest observation - smallest observation,for example, range=33.98 -(-11.28)=45.26 2. Determine,approximately,the number of classes K such that K is the smallest whole number that makes 2 greater than the number of observations, 97 in this case. Here , and thus K=8. 3. Divide the range by this K to determine, approximately the class width. 45.26/8=5.65 5.3 (Note that for convenience we use 5 as a class width. But you may try 6 or even 10 as class width.) 4. Determine class limits by beginning with a whole number. Make sure to include the smallest and largest observation. 5. If it is necessary to divide the data into more (fewer) groups, decrease (increase) the class width. Histogram: a graph made of rectangles whose areas are proportional to the relative frequencies of respective classes. To make histograms and ogives in MS Excel,Tools > Data Analysis… > Histogram.Then, enter the data range and the bin range. The bin range consists of the upper limits of the classes which in this example are -10.0001, -5.0001, -0.0001, 4.9999, 9.999, …, 29.9999, 34.9999.(What happens if you use -5, 0, 5, 10, …, instead?) • Histogram, if continues data there should be no gaps between the bars When you make histograms, you assume that the data are continuous data. Thus, you do not want to have a gap between two rectangles. To remove gaps, click on the histogram. Then you will see the panel “Format Data Series.” Next click “Options” and set the Gap Width to zero. You can get these using PHStat2, which yields the correct cumulative ogive. For details of how to make frequency distributions, histograms, and cumulative distribution ogives using MS Excel, refer to Chapter 2 Excel Guide (EG) on p. 85. HC Homework: In Example 5, construct a relative frequency distribution and sketch a corresponding histogram and the MGTOP 215 Page 2 HC Homework: In Example 5, construct a relative frequency distribution and sketch a corresponding histogram and the relative cumulative frequency using a class width of 10. Then compare this histogram with the histogram constructed in Example 4 and discuss which summarize the data best. MSL Homework: 2.11, 2.14, 2.16, 2.20 Open ended class: a class without either a lower limit or an upper limit. Polygon: another way of displaying a (relative) frequency distribution Ogive: a graph of a (relative) cumulative frequency distribution Example 6: The following is a frequency distribution of the number of cups of coffee sold by an Espresso stand on the corner of Grand and Main during a period of 50 days. Sketch a relative frequency histogram and a cumulative relative frequency ogive. Ex 6 30 20 10 wrong, don’t do 5 100 200 300 400 500 The height (y-axis) of a relative frequency histogram is called the density. The relative frequency of a class is the density • This is not the right way to start, you first that to make a (height) times the width of the class. frequency chart HC Homework: # of cups feq. Rel. feq. Width height rel. cum. Feq Sketch a relative frequency histogram and a cumulative relative frequency ogive for the following frequency 0-100 5 0.1 100 0.001 0.1 distribution. 100-200 10 0.2 100 0.002 0.3 200-300 30 0.6 100 0.006 0.9 300-500 5 0.1 200 0.005 1.0 • Find rel. feq. By diving feq by total feq in this case that being 50 • Find height by dividing rel. feq. By width. .006 Dot plot: .001 A stem and leaf plot is partly tabular and partly graphical way of summarizing data, and suitable for smaller data sets. In 100 200 300 400 500 this plot the first or leading digits serve as the stem and the trailing digits as the leaf Example 7. The following data represent the bounced check fee in dollars for a sample of 23 banks for direct-deposit 1 customers who maintain a $100 balance. Construct a dot plot and stem-and-leaf plot for the data. 0.1 We can obtain the following stem-and-leaf plot of the data in Example 4 using PHStat2: 0 100 200 300 400 500 MSL Homework: 2.33, 2.37, 2.40, 2.44 Commonshapes of distribution: symmetric skewed to the right (positively skewed) skewed to the left (negatively skewed) Mode: the location at which a relative frequency distribution peaks Modal class: the class that contains a mode. Unimodal MGTOP 215 Page 3 Bimodal HC Homework: Read Section 2.7 on misuses and commonerrors in visualizing data. Then find an example of graphics that is relevant to this section from newspapers, magazines, or the Internet, and make relevant commentson the example that you find. Good sources include Wall Street Journal, Business Week, and USA Today. This particular problem is due week from Wednesday of the week this Chapter 2 is finished. MGTOP 215 Page 4

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