790 CHAPTER 12 Statistics Example 8 Determining Quartiles Foot Locker is concerned about the high turnover of its sales staff. A survey was done to determine how long (in months) the sales staff had been in their current positions. The responses of 27 sales staff follow. Determine Q Q, , 1 2 and Q .3 25 3 71531361721 2 1142162319 21 920 5 8122714392418 610 Solution First we list the data from smallest to largest. 23567891011 12 14 15 16 17 18 19 20 21 21 23 24 25 27 31 36 39 42 Next we determine the median. Since there are 27 pieces of data, an odd number, the median will be the middle value. The middle value is 17, with 13 pieces of data less than 17 and 13 pieces of data greater than 17. Therefore, the median, Q ,2 is 17, shown in red. To determine Q ,1 the median of the lower half of the data, we need to determine the median of the 13 pieces of data that are less than Q .2 The middle value of the lower half of the data is 9. There are 6 pieces of data less than 9 and 6 pieces of data greater than 9. Therefore, Q1 is 9, shown in blue. To determine Q ,3 the median of the upper half of the data, we need to determine the median of the 13 pieces of data that are greater than 17, or Q .2 The middle value of the upper half of the data is 24. There are 6 pieces of data less than 24 and 6 pieces of data greater than 24. Therefore, Q3 is 24, shown in blue. 7 Now try Exercise 51 Learning Catalytics Keyword: Angel-SOM-12.3 (See Preface for additional details.) TECHNOLOGY TIP Several computer software programs and calculators can be used to determine the mean of a set of data. These programs and calculators can also provide other types of statistical information that we will discuss in this chapter. In this Technology Tip we will provide the instructions for using a software program called Microsoft Excel as well as information on how to use Texas Instruments TI-84 Plus graphing calculator and StatCrunch. In the example, we will use the data from Example 1, which represent the ages of nurses. Excel In our discussion, we will use the symbol > to indicate the next item to be selected from the list or menu of items. Begin by entering the five pieces of data in column A. Press the Enter key after each piece of data is entered. Next select Insert Function Statistical AVERAGE > …> > Then click the OK box at the bottom. The program will then generate a gray box, where you need to enter the data. In the area to the right of Number1 , you need to enter the data for which you want to determine the mean. Since you have already entered the data in column A, rows 1 to 5, if A1:A5 is not already listed, you can enter A1:A5 in the area to the right of Number1 . Then, at the bottom of the gray box, Formula Results 38 = is displayed. The 38 is the mean of the set of data. If you then press the OK box, the mean will be displayed in the cell where the cursor was located. If you do not want the mean displayed in a cell, press CANCEL. To determine the median or mode you follow a similar procedure, except that instead of selecting AVERAGE you would select MEDIAN or MODE, respectively. TI-84 Plus Graphing Calculators To enter the data, press STAT. Then highlight 1: Edit and press the ENTER key. If any data are currently listed in column L1 , move the cursor to L1 and press CLEAR and then
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