a. Class Freq. Complaint Freq.

31. Class

Freq. Cum. freq. Cum. rel. freq. 2 2 .050 14 16 .400

11 27

.675 8 35 .875 4 39 .975 39 .975 1 40 1.000

33. a.

640.5, 582.5 b. 610.5, 582.5 c. 591.2 d. 593.71

35. a.

, , . Deletion of the largest observation 18.0 causes and to be a bit smaller than . b. By at most 4.0 c. No; multiply the values of and by the conversion factor 12.2.

37. 39. a.

b. .383

41. a.

.7 b. Also .7 c. 13

43. 45. a.

; the deviations are b. .482, .694 c. .482 d. .482 47. . The magnitude of s indicates a sub- stantial amount of variation about the center a “representa- tive” deviation of roughly 25.

49. a.

56.80, 197.8040 b. .5016, .708

51. a.

1264.766, 35.564 b. .351, .593

53. a.

Bal: 1.121, 1.050, .536 Gr: 1.244, 1.100, .448 b. Typical ratios are quite similar for the two types. There is somewhat more variability in the Bal sample, due primarily to the two outliers one mild, one extreme. For Bal, there is substantial symmetry in the middle 50 but positive skew- ness overall. For Gr, there is substantial positive skew in the middle 50 and mild positive skewness overall.

55. a.

33 b. No c. Slight positive skewness in the middle half, but rather symmetric overall. The extent of variability appears sub- stantial. d. At most 32

57. a.

Yes. 125.8 is an extreme outlier and 250.2 is a mild outlier. b. In addition to the presence of outliers, there is positive skewness both in the middle 50 of the data and, excepting the outliers, overall. Except for the two outliers, there appears to be a relatively small amount of variability in the data.

59. a.

ED: .4, .10, 2.75, 2.65; Non-Ed: 1.60, .30, 7.90, 7.60 b. ED: 8.9 and 9.2 are mild outliers, and 11.7 and 21.0 are extreme outliers. x 5 116.2, s 5 25.75 .82, .32, 2.98, 2.38, .22 x 5 115.58 x | 5 68.0, x tr20 5 66.2, x tr30 5 67.5 x 5 1.0297, x| 5 1.009 x tr10 5 11.46 x | x x x tr x | x tr12.5 5 12.40 x | 5 12.50 x 5 12.55 24–,28 20–,24 16–,20 12–,16 8–,12 4–,8 0–,4 There are not outliers in the non-ED sample. c. Four outliers for ED, none for non-ED. Substantial posi- tive skewness in both samples; less variability in ED smaller f s , and non-ED observations tend to be somewhat larger than ED observations. 61. Outliers, both mild and extreme, only at 6 A . M . Distributions at other times are quite symmetric. Variability increases somewhat until 2 P . M . and then decreases slightly, and the same is true of “typical” gasoline-vapor coefficient values. 63. , , . A histogram consisting of 8 classes starting at 52, each of width 4, is bimodal but close to uni- modal with a positive skew. A boxplot shows no outliers, there is a very mild negative skew in the middle 50, and the upper whisker is much longer than the lower whisker. b. .9231, .9053 c. .48

67. a.

Female values are typically somewhat smaller than male values, and show somewhat more variability. An M boxplot shows negative skew whereas an F boxplot shows positive skew. b.

69. a. b.

189.14, 1.87

71. a.

The mean, median, and trimmed mean are virtually iden- tical, suggesting a substantial amount of symmetry in the data; the fact that the quartiles are roughly the same distance from the median and that the smallest and largest observa- tions are roughly equidistant from the center provides addi- tional support for symmetry. The standard deviation is quite small relative to the mean and median. b. See the comments of a. In addition, using as a yardstick, the two largest and three smallest observations are mild outliers. 73. small amount of variabil- ity, slight bit of skewness

75. a.

The “five-number summaries” , the two fourths, and the smallest and largest observations are identical and there are no outliers, so the three individual boxplots are identical. b. Differences in variability, nature of gaps, and existence of clusters for the three samples. c. No. Detail is lost.

77. c.

Representative depths are quite similar for the four types of soils—between 1.5 and 2. Data from the C and CL soils shows much more variability than for the other two types. The box- plots for the first three types show substantial positive skew- ness both in the middle 50 and overall. The boxplot for the SYCL soil shows negative skewness in the middle 50 and mild positive skewness overall. Finally, there are multiple out- liers for the first three types of soils, including extreme outliers.

79. a. c.

12.53, .532 x n1 1 5 nx n 1 x n1 1 n 1 1 x | x 5 .9255, s 5 .0809, x| 5 .93, 1.5Q3 2 Q1 y 5 ax 1 b , s y 2 5 a 2 s x 2 F: x tr10 5 3.24 M: x tr10 5 3.652 3.65 F: x 5 3.28, x| 5 3.15, s 5 .478, f s 5 .50 M: x 5 3.64, x| 5 3.70, s 5 .269, f s 5 .40 4 th 5 70.4, f s 5 12.6 upper lower 4 th 5 57.8 x 5 64.89, x| 5 64.70, s 5 7.803 Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook andor eChapters. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 81. A substantial positive skew assuming unimodality

83. a.

All points fall on a 45° line. Points fall below a 45° line. b. Points fall well below a 45° line, indicating a substantial positive skew. Chapter 2

1. a.

{1324, 3124, 1342, 3142, 1423, 1432, 4123, 4132, 2314, 2341, 3214, 3241, 2413, 2431, 4213, 4231}

b. c.

d. {1324, 1342, 1423, 1432, 2314, 2341, 3214, 3241, 2413, 2431, 4213, 4231}, contains no outcomes A and B are disjoint, {3124, 3142, 4123, 4132, 2314, 2341, 3214, 3241, 2413, 2431, 4213, 4231}

3. a. b.

c. d.

,

5. a.

{1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 2, 1, 2, 3, 1, 3, 1, 1, 3, 2, 1, 3, 3, 2, 1, 1, 2, 1, 2, 2, 1, 3, 2, 2, 1, 2, 2, 2, 2, 2, 3, 2, 3, 1, 2, 3, 2, 2, 3, 3, 3, 1, 1, 3, 1, 2, 3, 1, 3, 3, 2, 1, 3, 2, 2, 3, 2, 3, 3, 3, 1, 3, 3, 2, 3, 3, 3} b. {1, 1, 1, 2, 2, 2, 3, 3, 3} c. {1, 2, 3, 1, 3, 2, 2, 1, 3, 2, 3, 1, 3, 1, 2, 3, 2, 1} d. {1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 3, 3, 3, 1, 1, 3, 1, 3, 3, 3, 1, 3, 3, 3}

7. a.

There are 35 outcomes in . b. {AABABAB, AABAABB, AAABBAB, AAABABB, AAAABBB }

11. a.

.07 b. .30 c. .57

13. a.

.36 b. .64 c. .53 d. .47 e. .17 f. .75

15. a.

.572 b. .879

17. a.

There are statistical software packages other than SPSS and SAS. b. .70 c. .80 d. .20

19. a.

.8841 b. .0435

21. a.

.10 b. .18, .19 c. .41 d. .59 e. .31 f. .69 S S 5 B ¨ C 5 5SSF, SFS, SSS6 5 C, B ´ C 5 5SSF, SFS, FSS, SSS6 5 B, A ¨ C 5 5SSF, SFS6, A ´ C 5 5SSF, SFS, FSS, SSS6, C r 5 5FFF, FSF, FFS, FSS, SFF6 C 5 5SFS, SSF, SSS6 B 5 5SSF, SFS, FSS, SSS6 A 5 5SSF, SFS, FSS6 A r 5 A ¨ B A ´ B 5 B 5 52314, 2341, 3214, 3241, 2413, 2431, 4213, 42316 A 5 51324, 1342, 1423, 14326 S 5

23. a.

.067 b. .400 c. .933 d. .533

25. a.

.85 b. .15 c. .22 d. .35

27. a.

.1 b. .7 c. .6

29. a.

676; 1296 b. 17,576; 46,656 c. 456,976; 1,679,616 d. .942

31. a.

243 b. 3645 days roughly 10 yr

33. a.

1,816,214,400

b. 659,067,881,572,000 c. 9,072,000

35. a.

38,760, .0048 b. .0054 c. .9946 d. .2885

37. a.

60 b. 10 c. .0456

39. a.

.0839 b. .24975

41. a.

10,000 b. .9876 c. .0333 d. .0337 43. .000394, .00394, .00001539

45. a.

.447, .500, .200 b. .400, .447 c. .211

47. a.

.50 b. .50 c. .625 d. .375 e. .769

49. a.

.34, .40 b. .588 c. .50

51. a.

.436, b. .581 53. .083 55. .236

59. a.

.21 b. .455 c. .264, .462, .274

61. a.

.578, .278, .144 b. 0, .457, .543

63. b.

.54 c. .68 d. .74 e. .7941 65. .087, .652, .261 67. .000329; very uneasy.

69. a.

.126 b. .05 c. .1125 d. .2725 e. .5325 f. .2113

71. a.

.300 b. .820 c. .146 75. .401, .722

77. a.

.06235 b. .00421 79. .0059 Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook andor eChapters. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.