Chapter 42 Summarizing Data by Using Descriptive Statistics 345 The new Excel 2010 function RANK.AVG has the same syntax as the other RANK functions, but in the case of ties, RANK.AVG returns the average rank for all tied data points. For example, since the two scores of 98 ranked third and fourth, RANK.AVG returns 3.5 for each. I generated the average ranks by copying the formula RANK.AVG(C4,$C$4:$C$62,0) from E4 to E5:E62. What is the trimmed mean of a data set? Extreme skewness in a data set can distort the mean of the data set. In these situations, people usually use median as a measure of the data set’s typical value. The median, however, is unaffected by many changes in the data. For example, compare the following two data sets: Set 1: –5, –3, 0, 1, 3, 5, 7, 9, 11, 13, 15 Set 2: –20, –18, –15, –10, –8, 5, 6, 7, 8, 9, 10 These data sets have the same median (5), but the second data set should have a lower “typical” value than the rst. The Excel TRIMMEAN function is less distorted by extreme values than the AVERAGE function, but it is more inuenced by extreme values than the median. The formula TRIMMEAN(range,percent) computes the mean of a data set after deleting the data points at the top percent divided by 2 and bottom percent divided by 2. For example, applying the TRIMMEAN function with percent 10% converts the mean after deleting the top 5 percent and bottom 5 percent of the data. In cell F3 of the le Trimmean.xlsx, the formula TRIMMEAN(C4:C62,.10) computes the mean of the scores in C4:C62 after deleting the three highest and three lowest scores. (The result is 90.04.) In cell F4, the formula TRIMMEAN(C4:C62,.05) computes the mean of the scores in C4:C62 after deleting the top and bottom scores. This calculation occurs because .05*59 2.95 would in- dicate the deletion of 1.48 of the largest observations and 1.48 of the smallest. Rounding off 1.48 results in deleting only the top and bottom observations. (See Figure 42-7.) When I select a range of cells, is there an easy way to get a variety of statistics that describes the data in those cells? To see the solution to this question, select the cell range C4:C36 in the le Trimmean.xlsx. In the lower-right corner of your screen, the Excel status bar displays a cornucopia of statistics describing the numbers in the selected cell range. (See Figure 42-8.) For example, for the cell range C4:C36, the mean is 90.39, there are 33 numbers, the smallest value is 80, and the larg- est value is 100. If you right-click the status bar, you can change the displayed set of statistics. FIGURE 42-8 Stat st cs shown on the status bar. 346 Microsoft Excel 2010: Data Analysis and Business Modeling Why do nancial analysts often use the geometric mean to summarize the average return on a stock? The le Geommean.xlsx contains the annual returns of two ctitious stocks. (See Figure 42-9.) FIGURE 42-9 Geometr c mean. Cell C9 indicates that the average annual return on Stock 1 is 5 percent and the average annual return on Stock 2 is 10 percent. This would seem to indicate that Stock 2 is a better investment. If you think about it, however, what will probably happen with Stock 2 is that one year you will lose 50 percent and the next gain 70 percent. This means that every two years $1.00 becomes 1(1.7)(.5) .85. Because Stock 1 never loses money, you know that it is clearly the better investment. Using the geometric mean as a measure of average annual return helps to correctly conclude that Stock 1 is the better investment. The geometric mean of n numbers is simply the nth root of the product of the numbers. For example, the geometric mean of 1 and 4 is the square root of 4 (2), whereas the geometric mean of 1, 2, and 4 is the cube root of 8 (also 2). To use the geometric mean to calculate an average annual return on an investment, you add 1 to each annual return and take the geometric mean of the resulting numbers. Then subtract 1 from this result to obtain an estimate of the stock’s average annual return. The formula GEOMMEAN(range) nds the geometric mean of numbers in a range. So, to estimate the average annual return on each stock, you proceed as follows: 1. Compute 1+each annual return by copying from C12 to C12:D15 the formula 1+C5. 2. Copy from C16 to D16 the formula GEOMEAN(C12:C15)–1. The annual average return on Stock 1 is estimated to be 5 percent, and the annual average return on Stock 2 is –7.8 percent. Note that if Stock 2 yields the mean return of –7.8 percent during two consecutive years, $1 becomes 1(1–.078) 2 .85, which agrees with common sense. Chapter 42 Summarizing Data by Using Descriptive Statistics 347 Problems 1. Use the data in the le Stock.xlsx to generate descriptive statistics for Intel and GE stock. 2. Use your answer to Problem 1 to compare the monthly returns on Intel and GE stock. 3. City Power & Light produces voltage-regulating equipment in New York and ships the equipment to Chicago. A voltage regulator is considered acceptable if it can hold a voltage of 25–75 volts. The voltage held by each unit is measured in New York before each unit is shipped. The voltage is measured again when the unit arrives in Chicago. A sample of voltage measurements from each city is given in the le Citypower.xlsx. ❑ Using descriptive statistics, comment on what you have learned about the voltage held by units before and after shipment. ❑ What percentage of units are acceptable before and after shipping? ❑ Do you have any suggestions about how to improve the quality of City Power & Light’s regulators? ❑ Ten percent of all New York regulators have a voltage exceeding what value? ❑ Five percent of all New York regulators have a voltage less than or equal to what value? 4. In the le Decadeincome.xlsx, you are given a sample of incomes (in thousands of 1980 dollars) for a set of families sampled in 1980 and 1990. Assume that these families are representative of the whole United States. Republicans claim that the country was better off in 1990 than in 1980 because average income increased. Do you agree? 5. Use descriptive statistics to compare the annual returns on stocks, T-Bills, and corporate bonds. Use the data contained in the le Historicalinvest.xlsx. 6. In 1970 and 1971, eligibility for the U.S. armed services draft was determined on the basis of a draft lottery number. The number was determined by birth date. A total of 366 balls, one for each possible birth date, were placed in a container and shaken. The rst ball selected was given the number 1 in the lottery, and so on. Men whose birth- days corresponded to the lowest numbers were drafted rst. The le Draftlottery.xlsx contains the actual results of the 1970 and 1971 drawings. For example, in the 1970 drawing, January 1 received the number 305. Use descriptive statistics to demonstrate that the 1970 draft lottery was not random and the 1971 lottery was random (Hint: Use the AVERAGE and MEDIAN functions to compute the mean and median lottery number for each month.) 348 Microsoft Excel 2010: Data Analysis and Business Modeling 7. The le Jordan.xlsx gives the starting salaries (hypothetical) of all 1984 geography graduates from the University of North Carolina (UNC). What is your best estimate of a “typical” starting salary for a geography major? In reality, the major at UNC having the highest average starting salary in 1984 was geography because the great basketball player Michael Jordan was a geography major! 8. Use the LARGE or SMALL function to sort the annual stock returns in the le Historicalinvest.xlsx. What advantage does this method of sorting have over clicking the Sort button? 9. Compare the mean, median, and trimmed mean (trimming 10 percent of the data) of the annual returns on stocks, T-Bills, and corporate bonds given in the le Historicalinvest.xlsx. 10. Use the geometric mean to estimate the mean annual return on stocks, bonds, and T-Bills in the le Historicalinvest.xlsx. 11. The le Dow.xlsx contains monthly returns on the 30 Dow stocks during the last 20 years. Use this data to determine the three stocks with the largest mean monthly returns. 12. Using the Dow.xlsx data again, determine the three stocks with the most risk or variability. 13. Using the Dow.xlsx data, determine the three stocks with the highest skew. 14. Using the Dow.xlsx data, how do the trimmed-mean returns (trim off 10 percent of the returns) differ from the overall mean returns? 15. The le Incomedata.xlsx contains incomes of a representative sample of Americans in the years 1975, 1985, 1995, and 2005. Describe how U.S. personal income has changed over this time period. 16. The le Coltsdata.xlsx contains yards gained by the 2006 Indianapolis Colts on each rushing and passing play. Describe how the outcomes of rushing plays and passing plays differ. 349 Chapter 43 Using PivotTables and Slicers to Describe Data Questions answered in this chapter: ■ What is a PivotTable? ■ How can I use a PivotTable to summarize grocery sales at several grocery stores? ■ What PivotTable layouts are available in Excel 2010? ■ Why is a PivotTable called a PivotTable? ■ How can I easily change the format in a PivotTable? ■ How can I collapse and expand elds? ■ How do I sort and lter PivotTable elds? ■ How do I summarize a PivotTable by using a PivotChart? ■ How do I use the Report Filter section of the PivotTable? ■ How do Excel 2010 slicers work? ■ How do I add blank rows or hide subtotals in a PivotTable? ■ How do I apply conditional formatting to a PivotTable? ■ How can I update my calculations when I add new data? ■ I work for a small travel agency for which I need to mass-mail a travel brochure. My funds are limited, so I want to mail the brochure to people who spend the most money on travel. From information in a random sample of 925 people, I know the gender, the age, and the amount these people spent on travel last year. How can I use this data to determine how gender and age inuence a person’s travel expenditures? What can I conclude about the type of person to whom I should mail the brochure? ■ I’m doing market research about Volvo Cross Country Wagons. I need to determine what factors inuence the likelihood that a family will purchase a station wagon. From information in a large sample of families, I know the family size (large or small) and the family income (high or low). How can I determine how family size and income inuence the likelihood that a family will purchase a station wagon? 350 Microsoft Excel 2010: Data Analysis and Business Modeling ■ I work for a manufacturer that sells microchips globally. I’m given monthly actual and predicted sales for Canada, France, and the United States for Chip 1, Chip 2, and Chip 3. I’m also given the variance, or difference, between actual and budgeted revenues. For each month and each combination of country and product, I’d like to display the following data: actual revenue, budgeted revenue, actual variance, actual revenue as a percentage of annual revenue, and variance as a percentage of budgeted revenue. How can I display this information? ■ What is a calculated eld? ■ How do I use a report lter or slicer? ■ How do I group items in a PivotTable? ■ What is a calculated item? ■ What is “drilling down”? ■ I often have to use specic data in a PivotTable to determine prot, such as the April sales in France of Chip 1. Unfortunately, this data moves around when new elds are added to my PivotTable. Does Excel have a function that enables me to always extract April’s Chip 1 sales in France from the PivotTable? Answers to This Chapter’s Questions What is a PivotTable? In numerous business situations, you need to analyze, or “slice and dice,” your data to gain important insights. Imagine that you sell different grocery products in different stores at different points in time. You might have hundreds of thousands of data points to track. PivotTables let you quickly summarize your data in almost any way imaginable. For example, for your grocery store data, you could use a PivotTable to quickly determine the following: ■ Amount spent per year in each store on each product ■ Total spending at each store ■ Total spending for each year In a travel agency, as another example, you might slice data so that you can determine whether the average amount spent on travel is inuenced by age or gender or by both factors. In analyzing automobile purchases, you’d like to compare the fraction of large families that buy a station wagon to the fraction of small families that purchase a station wagon. For a microchip manufacturer, you’d like to determine total Chip 1 sales in France, for example, during April, and so on. A PivotTable is an incredibly powerful tool that you can use to slice and dice data. The easiest way to understand how a PivotTable works is to walk through some carefully constructed examples, so let’s get started! I’ll begin with Chapter 43 Using PivotTables and Slicers to Describe Data 351 an introductory example and then illustrate many advanced PivotTable features through subsequent examples. Note Exce 2010 conta ns a new feature ca ed slicers that make t much eas er to use P votTab es to exam ne your data from many perspect ves I d scuss s cers ater n the chapter How can I use a PivotTable to summarize grocery sales at several grocery stores? The Data worksheet in the le Groceriespt.xlsx contains more than 900 rows of sales data. (See Figure 43-1.) Each row contains the number of units sold and revenue of a product at a store, as well as the month and year of the sale. The product group (either fruit, milk, cereal, or ice cream) is also included. You would like to see a breakdown of sales during each year of each product group and product at each store. You would also like to be able to show this breakdown during any subset of months in a given year (for example, what the sales were during January–June). FIGURE 43-1 Data for the grocery P votTab e examp e. Before creating a PivotTable, you must have headings in the rst row of your data. Notice that the grocery data contains headings (Year, Month, Store, Group, Product, Units, and Revenue) in row 2. Place your cursor anywhere in the data, and then click PivotTable in the Tables group on the Insert tab. Excel opens the Create PivotTable dialog box, shown in Figure 43-2, and makes an assumption about your data range. (In this case, Excel correctly guessed that the data range was C2:I924.) By selecting Use An External Data Source, you can also refer to a database as a source for a PivotTable. 352 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 43-2 The Create P votTab e d a og box. After you click OK, you see the PivotTable Field List shown in Figure 43-3. FIGURE 43-3 The P votTab e F e d L st. You ll in the PivotTable Field List by dragging PivotTable headings, or elds, into the boxes, or zones. This step is critical to ensuring that the PivotTable will summarize and display the data in the manner you want. The four zones are as follows: ■ Row Labels Fields dragged here are listed on the left side of the table in the order in which they are added to the box. For example, I dragged to the Row Labels box the elds Year, Group, Product, and Store, in that order. This causes Excel to summarize data rst by year, then for each product group within a given year, then by product within each group, and nally each product by store. You can at any time drag a eld to a different zone or reorder the elds within a zone by dragging a eld up or down in a zone or by clicking the arrow to the right of the eld label. Chapter 43 Using PivotTables and Slicers to Describe Data 353 ■ Column Labels Fields dragged here have their values listed across the top row of the PivotTable. To start out this example, we have no elds in the Column Labels zone. ■ Values Fields dragged here are summarized mathematically in the table. I dragged Units and Revenue (in that order) to this zone. Excel tries to guess what kind of cal- culation you want to perform on a eld. In this example, Excel guesses that Revenue and Units should be summed, which happens to be correct. If you want to change the method of calculation for a data eld to an average, a count, or something else, simply click the data eld and choose Value Field Settings. I give an example of how to use the Value Field Settings command later in the chapter. ■ Report Filter Beginning in Excel 2007, Report Filter is the new name for the old Page Field area. For elds dragged to the Report Filter area, you can easily pick any subset of the eld values so that the PivotTable shows calculations based only on that subset. In this example, I dragged Month to the Report Filter area. That lets me easily select any subset of months, for example January–June, and the calculations are based on only those months. Slicers in Excel 2010 make report lters virtually obsolete. The completed PivotTable Field List is shown in Figure 43-4. The resulting PivotTable is shown in Figure 43-5 and in the All Row Fields worksheet of the workbook Groceriespt.xlsx. In row 6, you can see that 233,161 units were sold for $702,395.82 in 2007. Tip Here s some adv ce about nav gat ng workbooks ( ke the one n th s examp e) conta n ng many worksheets In the ower-r ght corner of the Exce w ndow (to the eft of the worksheet names), you w see four arrows C ck ng the eft-most arrow takes you to the rst worksheet; c ck ng the r ght-most arrow shows the ast worksheet; and c ck ng the other arrows moves you one worksheet to the eft or r ght Note To see the e d st, you need to be n a e d n the P votTab e If you do not see the e d st, r ght-c ck any ce n the P votTab e and se ect Show F e d L st FIGURE 43-4 Comp eted P votTab e F e d L st. 354 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 43-5 The Grocery P votTab e n compact form. What PivotTable layouts are available in Excel 2010? The PivotTable layout shown in Figure 43-5 is called the compact form. In the compact form, the row elds are shown one on top of another. To change the layout, rst place your cursor anywhere within the table. On the Design tab, in the Layout Group, click Report Layout, and choose one of the following: Show In Compact Form (see Figure 43-5), Show In Outline Form (see Figure 43-6 and the Outline Form worksheet), or Show In Tabular Form (Figure 43-7 and the Tabular Form worksheet). FIGURE 43-6 The out ne format. [...]... thout tota s  364 Microsoft Excel 2010: Data Analysis and Business Modeling How do I apply conditional formatting to a PivotTable? Suppose you want to apply data bars to the Units column in the grocery PivotTable One problem you’ll encounter is that subtotals and grand totals will have large data bars and also ­ make the other data bars smaller than they should be It’s better to have the data bars apply... Select the Row Labels filtering icon, select Value Filters, Top 10, and fill in the dialog box as shown in Figure 43- 16  360 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 43- 16 Configur ng the Top 10 F ter d a og box to show customers generat ng 50 percent of revenue The resulting PivotTable is in the Top half worksheet and shown in Figure 43-17 As you can see, the top 14 customers generate... tend to spend about the same amount on travel This view of the data does not help d ­ etermine who you should mail your brochure to  368 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 43-31  Use the Group And Show Deta command to group deta ed records Finally, let’s get a breakdown of average travel spending by age, for men and women s ­ eparately All you have to do is drag Gender to... (see the data worksheet) For example, in the U.S in January, sales of Chip 1 totaled $4,000, although sales of $5,454 were predicted This yielded a v ­ ariance of –$1,454 372 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 43-38  Ch p data from d fferent countr es for d fferent months show ng actua , budget, and var ance revenues For each month and each combination of country and product,... buy a station wagon FIGURE 43-34  Data co ected about ncome, fam y s ze, and the purchase of a stat on wagon 370 Microsoft Excel 2010: Data Analysis and Business Modeling You want to determine how family size and income influence the likelihood that a family will purchase a station wagon The trick is to look at how income affects purchases for each f ­ amily size and how family size affects purchases... gender for each age group 366 Microsoft Excel 2010: Data Analysis and Business Modeling The data is included on the Data worksheet in the file Traveldata.xlsx, and a sample is shown in Figure 43- 26 For example, the first person is a 44-year-old male who spent $997 on travel Let’s first get a breakdown of spending by gender Begin by selecting Insert PivotTable Excel extracts the range A2:D927 After clicking... shown in Figure 44-45 by selecting the Product and Country fields Selecting Chip 2 from the Product slicer and France from the Country slicer yields the relevant computations for all transactions involving Chip 2 in France If you want to resize a slicer, hold down the Ctrl key, and then resize the slicer 3 76 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 43-45  Sa es of Ch p 2 n France... any cell containing a year (for example, A5), and choose Sort Smallest To Largest from the available options At the bottom of the filtering options dialog box, you can also select any subset of products ­ to be displayed You may want to first clear Select All and then select the products you want to show 358 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 43-12  P votTab e fi ter ng... and select Number Format from the Value Field Settings dialog box Then apply the format you want For example, in the Formatted $s worksheet, I formatted the Revenue field as currency by double-clicking the Sum Of Revenue heading and applying a currency format You can also change the format of a value field by clicking the arrow to the right of the Value 3 56 Microsoft Excel 2010: Data Analysis and Business. .. list, select % Of Column and rename this field as Sum Of Revenue2, as shown in Figure 43-40 FIGURE 43-40  Creat ng each month s percentage of annua revenue You now obtain the PivotTable shown in Figure 43-41 (See the 2nd Table worksheet.) January sales provided 8.53 percent of revenue Total revenue for the year was $1,0 26, 278 374 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 43-41  . icon, select Value Filters, Top 10, and ll in the dialog box as shown in Figure 43- 16. 360 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 43- 16 Congur ng the Top 10 F ter d a. lottery was random (Hint: Use the AVERAGE and MEDIAN functions to compute the mean and median lottery number for each month.) 348 Microsoft Excel 2010: Data Analysis and Business Modeling 7 43-20. The chart shows that milk sales were highest in 2005 and lowest in 20 06. 362 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 43-20 P votChart for un t group sa es trend. How