Chapter 2: Graphs, Charts, and Tables--Describing Your Data

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50 CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA TRY PROBLEM 2.12 two variables: payment method (cash or charge) and number of pizzas purchased. The manager wishes to develop a joint frequency distribution to better understand the buying habits of his customers. To do this, he can use the following steps: Step 1 Obtain the data. The paired data for the two variables for a sample of 12 customers are obtained. Customer Payment Method Pizzas Purchased 1 Charge 2 2 Charge 1 3 Cash 2 4 Charge 2 5 Charge 1 6 Cash 1 7 Cash 3 8 Charge 1 9 Charge 3 10 Cash 2 11 Cash 1 12 Charge 1 Step 2 Construct the rows and columns of the joint frequency table. The row variable will be the payment method, and two rows will be used, corresponding to the two payment methods. The column variable is pizzas purchased, and it will have three levels, because the data for this variable contain only the values 1, 2, and 3. (Note, if a variable is continuous, classes should be formed using the methods discussed in Example 2-3.) Pizzas Purchased 1 2 3 Payment Charge Cash Step 3 Count the number of joint occurrences at each row level and each column level for all combinations of row and column values and place these frequencies in the appropriate cells. Pizzas Purchased Payment 1 2 3 Total Charge 4 2 1 7 Cash 2 2 1 5 Total 6 4 2 12 Step 4 Calculate the row and column totals (see Step 3). The manager can now see that for this sample, most people charged their purchase (seven people) and most people purchased only one pizza (six people). Likewise, four people both purchased one pizza and charged their purchase.
CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA 51 Business Application Excel and Minitab Tutorial CAPITAL CREDIT UNION (CONTINUED) Recall that the Capital Credit Union discussed earlier was interested in evaluating the success of its new credit card. Figures 2.5 and 2.6 showed the frequency distribution and histogram for a sample of customer credit card balances. Although this information is useful, the managers would like to know more. Specifically, what does the credit card balance distribution look like for male versus female cardholders? One way to approach this is to sort the data by the gender variable and develop frequency distributions and histograms for males and females separately. You could then make a visual comparison of the two to determine what, if any, difference exists between males and females. However, an alternative approach is to jointly analyze the two variables: gender and credit card balance. Although the process is different for Excel and Minitab, both software packages provide methods for analyzing two variables jointly. In Figure 2.5, we constructed the frequency distribution for the 300 credit card balances using 10 classes. The class width was set at $150. Figure 2.7 shows a table that is called a joint frequency distribution. This type of table is also called a cross-tabulation table. 1 The Capital Credit Union managers can use a joint frequency table to analyze the credit card balances for males versus females. For instance, for the 61 customers with balances of $540 to $689, Figure 2.7 shows that 45 were males and 16 were females. Previously, we discussed the concept of relative frequency (proportions, which Excel converts to percentages) as a useful tool for making comparisons between two data sets. In this example, comparisons between males and females would be easier if the frequencies were converted to proportions (or percentages). The result is the joint relative frequency table shown in Figure 2.8. Notice that the percentages in each cell are percentages of the FIGURE 2.7 Excel 2007 Output of the Capital Credit Union Joint Frequency Distribution Excel 2007 Instructions. 1. Open file: Captital.xls. 2. Place cursor anywhere in the data. 3. On the Insert tab, click on PivotTable and click OK. 4. Drag Credit Card Account Balance to “Drop Row Field Here” area. 5. Right-click in Credit Card Account Balance numbers and click Group. 6. Change Start at to 90. Change End to 1589. Change By to 150. 7. Drag Gender to “Drop Column Fields Here” area. 8. Drag Credit Card Account Balance to “Drop Data Items Here” area. 9. Click on “Drop Page Fields Here” area to close it. Minitab Instructions (for similar results): 1. Open file: Capital.MTW. 2. Click on Data > Code > Numeric to Text. 3. Under Code data from columns, select data column. 4. Under Into columns, specify destination column; Classes. 5. In Original values, define each data class range. 6. In New, specify code for each class. 7. Click OK. 8. Click on Stat > Tables > Cross Tabulation and Chi-Square. 9. Under Categorical Variables For rows enter Classes column and For columns enter Gender column. 10. Under Display check Column Frequency. 11. Click OK. 1 In Excel, the joint frequency distribution is developed using a tool called Pivot tables. In Minitab, the joint frequency distributions are constructed using the Cross Tabulation option.
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Chapter 2: Graphs, Charts, and Tables--Describing Your Data

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