802 CHAPTER 12 Statistics TECHNOLOGY TIP In this Technology Tip , we will explain how to determine the standard deviation using Excel the Texas Instrument TI-84 Plus graphing calculator, as well as StatCrunch. In our illustration, we will use the data from Example 3, which represent the prices of nine stocks on the New York Stock Exchange. Excel The instructions used to determine the standard deviation are very similar to those used to determine the mean in the Technology Tip on page 790 in Section 12.3. Please read that material now. Then enter the nine pieces of data in columns − A1 A9 and press the ENTER key. Now select the following: Insert Function Statistical STDEV > …> > Then click the OK box. 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 standard deviation. Since you have already entered the data in column A, rows 1 to 9, if A1:A9 is not already listed, you can enter A1:A9 in the area to the right of Number1 . At the bottom of the gray box, Formula Results 27.00925767, = which is the standard deviation, is displayed. If you click OK, Excel will place the standard deviation in cell A10. TI-84 Plus Graphing Calculators To determine the standard deviation on Texas Instruments graphing calculators, follow the instructions for determining the mean in the Technology Tip on page 790 in Section 12.3. As explained there, press > > STAT EDIT ENTER. Remove existing data by highlighting L1 and then pressing > CLEAR ENTER. Then enter the nine pieces of data, pressing the ENTER key after each entry. Then press > > > STAT CALC ENTER ENTER. The fourth statistic down is S 27.00925767. x = This value is the standard deviation. StatCrunch (available in Mylab Math and separately) To compute this standard deviation, follow the steps in the Technology Tip on page 791 except make sure that standard deviation is selected in Step 4. You will see the standard deviation is 27.009. Exercises Warm Up Exercises In Exercises 1– 6, fill in the blank with an appropriate word, phrase, or symbol(s). 1. Measures of dispersion are used to indicate the spread or _______ of the data. Variability 2. The difference between the highest and lowest values in a set of data is called the _______. Range 3. The measure of dispersion that measures how much the data differ from the mean is called the _______. Standard deviation 4. The symbol σ is used to indicate the standard deviation of a(n) _______. Population 5. The symbol s is used to indicate the standard deviation of a(n) _______. Sample 6. The standard deviation of a set of data in which all the data values are the same is _______. 0 Many of the exercises in this section are designed so that they can be done by hand or by using an appropriate form of technology (graphing calculator, spreadsheet, or StatCrunch). Practice the Skills In Exercises 7–12, determine the range of the set of data. 7. 15, 8, 7, 25, 36, 2 34 8. 45, 6, 48, 52, 30, 12, 65 59 9. 150, 350, 210, 80, 175, 90 270 10. 87, 12, 78, 100, 47, 25 88 11. 25, 27, 32, 37, 16, 18 21 12. 60, 58, 62, 48, 51, 72, 70 24 SECTION 12.4 Instructor Resources for Section 12.4 in MyLab Math • Objective-Level Videos 12.4 • Animation: Data Sets: Mean and Standard Deviation • PowerPoint Lecture Slides 12.4 • MyLab Exercises and Assignments 12.4
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