12.3 Measures of Central Tendency and Position 791 the ENTER key. This step will eliminate all data from column L1. Now enter the data in column L1. After you enter each piece of data, press the ENTER key. After all the data have been entered, press STAT. Then highlight CALC. At this point, 1: 1-Var Stats should be highlighted. Press the ENTER key twice. You will now see x 38. = Thus, the mean is 38. Several other descriptive statistics that we will discuss shortly are also shown. If you scroll down, you will eventually see the values of Q,1 the median, and Q .3 StatCrunch (available in MyLab Math and separately) 1. To compute the mean and median, go to the StatCrunch website and then select Open StatCrunch in the top menu. 2. Enter your data into the spreadsheet under var 1. 3. Click Applets in the top menu. Select Mean/SD vs Median/lQR from the dropdown menu. 4. Click on the radio button Data Table. From the select column dropdown menu, select var 1. Make sure mean and median are selected under Statistics Shown. 5. Click Compute. You will see that the mean is 38 and the median is 37. Exercises Warm Up Exercises In Exercises 1–10, fill in the blank with an appropriate word, phrase, or symbol(s). 1. A number that is representative of a set of data is called a(n) _______. Average 2. Averages are referred to as measures of central _______. Tendency 3. The average that is determined by summing the data and then dividing the sum by the number of pieces of data is called the _______. Mean 4. The value in the middle of a set of ranked data is called the _______. Median 5. The piece of data that occurs most frequently in a set of data is called the _______. Mode 6. The value halfway between the lowest and highest values in a set of data is called the _______. Midrange 7. The measures of position that divide a set of data into four equal parts are called _______. Quartiles 8. The measures of position that divide a set of data into 100 equal parts are called _______. Percentiles 9. a) The symbol for the sample mean is _______. x b) The symbol for the population mean is _______. μ 10. a) Another name for the 25th percentile is the _______ quartile. First b) Another name for the 50th percentile is the _______ quartile. Second c) Another name for the 75th percentile is the _______ quartile. Third Many of the exercises in this section are designed so that they can be done by using an appropriate form of technology (graphing calculator, spreadsheet, or StatCrunch). Practice the Skills In Exercises 11–30, where appropriate, round your answer to the nearest tenth. In Exercises 11–14, determine the mean. 11. 9, 10, 10, 12, 14, 14, 14, 25, 27 15 12. 8, 9, 11, 14, 16, 25, 29 16 13. 4, 11, 7, 15, 29, 32, 34, 16 18.5 14. 8, 10, 14, 15, 13, 15, 17, 19 13.9 In Exercises 15 – 18, determine the median. 15. 61, 67, 79, 40, 85, 37, 81 67 16. 1, 7, 11, 27, 36, 14, 12, 9, 1 11 17. 1, 3, 5, 7, 9, 11, 13, 15 8 18. 2, 25, 11, 6, 7, 9, 8, 10, 14, 20 9.5 In Exercises 19–22, determine the mode. 19. 2, 2, 8, 11, 5, 7, 9, 13, 3, 2, 3 2 20. 4, 16, 15, 12, 4, 7, 8, 12, 4, 15 4 21. 5, 15, 5, 15, 20, 25, 30 5 and 15 22. 2, 4, 6, 8, 10, 12, 14 no mode SECTION 12.3 Instructor Resources for Section 12.3 in MyLab Math • Objective-Level Videos 12.3 • Animation: Data Sets: Mean, Median, Mode • PowerPoint Lecture Slides 12.3 • MyLab Exercises and Assignments 12.3
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