136 Chapter 3 Numerical Summaries of Data EXCEL Computing Quartiles Step 1. Enter the data from Table 3.14 in Column A. Step 2. Select the Insert Function icon fx and highlight Statistical in the category field. Step 3. Highlight QUARTILE.EXC and press OK. Enter the range of cells that contain the data from Table 3.14 in the Array field. In the Quart field, enter 1 for Q1, 2 for Q2, or 3 for Q3. Step 4. Click OK. SECTION 3.3 Exercises Exercises 1–4 are the Check Your Understanding exercises located within the section. Understanding the Concepts In Exercises 5–8, fill in each blank with the appropriate word or phrase. 5. divide the data set approximately into quarters. 6. The median is the same as the quartile. 7. The quantity Q3 − Q1 is known as the . 8. A value that is considerably larger or smaller than most of the values in a data set is called an . In Exercises 9–12, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement. 9. The third quartile, Q3, separates the lowest 25% of the data from the highest 75%. 10. The 25th percentile is the same as the first quartile. 11. The five-number summary consists of the minimum, the first quartile, the mode, the third quartile, and the maximum. 12. In a boxplot, if the lower whisker is much longer than the upper whisker, then the data are skewed to the left. Practicing the Skills 13. A population has mean μ = 7 and standard deviation σ = 2. a. Find the z-score for a population value of 5. b. Find the z-score for a population value of 10. c. What number has a z-score of 2? 14. A population has mean μ = 25 and standard deviation σ = 4. a. Find the z-score for a population value of 16. b. Find the z-score for a population value of 31. c. What number has a z-score of 2.5? In Exercises 15 and 16, identify the outlier. Then tell whether the outlier seems certain to be due to an error, or whether it could conceivably be correct. 15. A rock is weighed five times. The readings in grams are 48.5, 47.2, 4.91, 49.5, and 46.3. 16. A sociologist samples five families in a certain town and records their annual income. The incomes are $34,000, $57,000, $13,000, $1,200,000, and $62,000. 17. For the data set 37 82 20 25 31 10 41 44 4 36 68 a. Find the first and third quartiles. b. Find the IQR. c. Find the upper and lower outlier boundaries. d. List all the values, if any, that are classified as outliers. 18. For the data set 15 7 2 4 4 3 4 3 4 25 4 9 3 12 2 8 3 2 2 6 7 3 10 4 5 4 a. Find the first and third quartiles. b. Find the IQR. c. Find the upper and lower outlier boundaries. d. List all the values, if any, that are classified as outliers. 19. For the data set 2 2 2 2 5 7 8 8 9 9 14 14 14 16 19 20 21 22 22 24 24 27 32 33 33 33 34 34 35 35 35 37 38 38 38 40 40 40 41 42 46 47 48 48 48 48 48 49 a. Find the 58th percentile. b. Find the 22nd percentile. c. Find the 78th percentile. d. Find the 15th percentile. 20. For the data set 1 5 8 8 8 11 13 14 15 15 16 17 20 23 24 25 25 26 26 29 31 34 35 35 38 44 45 47 47 51 53 53 54 55 55 57 57 59 60 62 65 69 70 75 75 76 78 79 81 83 83 84 89 91 92 93 93 96 96 99 a. Find the 80th percentile. b. Find the 43rd percentile. c. Find the 18th percentile. d. Find the 65th percentile. Working with the Concepts 21. Standardized tests: In 2008, the mean score on the ACT test was 21.1 and the standard deviation was 5.0. The mean score on the SAT mathematics test was 515 and the standard deviation was 116. The distributions of both scores were approximately bell-shaped.
navidi_monk_essential_statistics_1e_ch1_3
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