Secto.. 6l 34 6h 667899 7l 44 7h Stem=Tes 8l 344 Leaf=Oes 8h 5557899 9l 3 9h 58 Ths dsplay brgs out the gap the data: There are o scores the hgh 7's. 6. a. beams cylders 9 5 8 88533 6 6 98877643 7 488 7 8 3359 77 9 78 7 863 6 3 4 The data appears to be slghtly skewed to the rght, or postvely skewed. The value of 4. appears to be a outler. Three out of the twety, 3/ or.5 of the observatos eceed Mpa.
b. The majorty of observatos are betwee 5 ad 9 Mpa for both beams ad cylders, wth the modal class the 7 Mpa rage. The observatos for cylders are more varable, or spread out, ad the mamum value of the cylder observatos s hgher. c. Dot Plot... :.. :.:... :... -+---------+---------+---------+---------+---------+-----cylder 6. 7.5 9..5. 3.5 9. a. From ths frequecy dstrbuto, the proporto of wafers that cotaed at least oe partcle s (-)/ =.99, or 99%. Note that t s much easer to subtract (whch s the umber of wafers that cota partcles) from tha t would be to add all the frequeces for,, 3, partcles. I a smlar fasho, the proporto cotag at least 5 partcles s ( - --3-- )/ = 7/ =.7, or, 7%. b. The proporto cotag betwee 5 ad partcles s (5+8+++4+5)/ = 64/ =.64, or 64%. The proporto that cota strctly betwee 5 ad (meag strctly more tha 5 ad strctly less tha ) s (8+++4)/ = 44/ =.44, or 44%. c. The followg hstogram was costructed usg Mtab. The data was etered usg the same techque metoed the aswer to eercse 8(a). The hstogram s almost symmetrc ad umodal; however, t has a few relatve mama (.e., modes) ad has a very slght postve skew. Relatve frequecy... 5 Number of partcles 5
Desty 6. a. Yes: the proporto of sampled agles smaller tha 5 s.77 +.66 +.75 =.58. b. The proporto of sampled agles at least 3 s.78 +.44 +.3 =.5. c. The proporto of agles betwee ad 5 s roughly.75 +.36 + (..94)/ =.48. d. The dstrbuto of msoretato agles s heavly postvely skewed. Though agles ca rage from to 9, early 85% of all agles are less tha 3. Wthout more precse formato, we caot tell f the data cota outlers..4 Hstogram of Agle.3... 4 Agle 9
7. a. The edpots of the class tervals overlap. For eample, the value 5 falls both of the tervals 5 ad 5. b. Class Iterval Frequecy Relatve Frequecy - < 5 9.8 5 - < 9.38 - < 5. 5 - < 4.8 - < 5.4 5 - < 3.4 3 - < 35. 35 - < 4. >= 4. 5. 5 5 5 3 35 4 45 5 55 6 lfetme The dstrbuto s skewed to the rght, or postvely skewed. There s a gap the hstogram, ad what appears to be a outler the 5 55 terval.
c. Class Iterval Frequecy Relatve Frequecy.5 - <.75.4.75 - < 3.5.4 3.5 - < 3.75 3.6 3.75 - < 4.5 8.6 4.5 - < 4.75 8.36 4.75 - < 5.5. 5.5 - < 5.75 4.8 5.75 - < 6.5 3.6.5.75 3.5 3.75 4.5 4.75 5.5 5.75 6.5 l lfetme The dstrbuto of the atural logs of the orgal data s much more symmetrc tha the orgal. d. The proporto of lfetme observatos ths sample that are less tha s.8 +.38 =.56, ad the proporto that s at least s.4 +.4 +. +. +. =.4.
Cout of complat 9. Complat Frequecy Relatve Frequecy B 7.67 C 3.5 F 9.5 J.667 M 4.667 N 6. O.35 6. B C F J M N O complat Secto.3 35. a. The sample mea s = (.4/8) =.55. The sample sze ( = 8) s eve. Therefore, the sample meda s the average of the (/) ad (/) + values. By sortg the 8 values order, from smallest to largest: 8. 8.9.. 3. 4.5 5. 8., the forth ad ffth values are ad 3. The sample meda s (. + 3.)/ =.5. The.5% trmmed mea requres that we frst trm (.5)() or value from the eds of the ordered data set. The we average the remag 6 values. The.5% trmmed mea tr(.5) s 74.4/6 =.4.
All three measures of ceter are smlar, dcatg lttle skewess to the data set. b. The smallest value (8.) could be creased to ay umber below. (a chage of less tha 4.) wthout affectg the value of the sample meda. c. The values obtaed part (a) ca be used drectly. For eample, the sample mea of.55 ps could be re-epressed as ks (.55 s) 5.7ks. ps. 36. a. A stem-ad leaf dsplay of ths data appears below: 3 55 stem: oes 33 49 leaf: teths 34 35 6699 36 34469 37 3345 38 9 39 347 4 3 4 4 4 The dsplay s reasoably symmetrc, so the mea ad meda wll be close. b. The sample mea s = 9638/6 = 37.7. The sample meda s ~ = (369+37)/ = 369.5. c. The largest value (curretly 44) could be creased by ay amout. Dog so wll ot chage the fact that the mddle two observatos are 369 ad 7, ad hece, the meda wll ot chage.
However, the value = 44 ca ot be chaged to a umber less tha 37 (a chage of 44-37 = 54) sce that wll lower the values(s) of the two mddle observatos. d. Epressed mutes, the mea s (37.7 sec)/(6 sec) = 6.8 m; the meda s 6.6 m. 4. a. 7. 7 b.. 7 = proporto of successes s c. 8 5. so s = (.8)(5) = total of successes 7 = 3 of the ew cars would have to be successes (57 79) 43. meda = 68., % trmmed mea = 66., 3% trmmed mea = 67.5. Secto.4 45. a. = = 577.9/5 = 5.58. Devatos from the mea: 6.4-5.58 =.8, 5.9-5.58 =.3, 4.6-5.58 = -.98, 5. - 5.58 = -.38, ad 5.8-5.58 =.. b. s = [(.8) + (.3) + (-.98) + (-.38) + (.) ]/(5-) =.98/4 =.48, so s =.694. c. = 66,795.6, so s = = [66,795.6 - (577.9) /5]/4 =.98/4 =.48. d. Subtractg from all values gves 5. 58, all devatos are the same as part b, ad the trasformed varace s detcal to that of part b.
5. a. 563 ad 368, 5, so [368,5 (563) /9] s 64.766 ad s 35. 564 8 c b. If y = tme mutes, the y = c where, so 6 64.766 35.564 s y c s.35 ad s y cs. 593 36 6 53. a. lower half:.34.43.6.74.74.75.78 3. 3.46 upper half: 3.46 3.56 3.65 3.85 3.88 3.93 4. 4.33 4.5 Thus the lower fourth s.74 ad the upper fourth s 3.88. b. f 3.88.74. 4 s c. f s would t chage, sce creasg the two largest values does ot affect the upper fourth. d. By at most.4 (that s, to aythg ot eceedg.74), sce the t wll ot chage the lower fourth. e. Sce s ow eve, the lower half cossts of the smallest 9 observatos ad the upper half cossts of the largest 9. Wth the lower fourth =.74 ad the upper fourth = 3.93, f. 9. s 59. a. ED: meda =.4 (the 4 th value the sorted lst of data). The lower quartle (meda of the lower half of the data, cludg the meda, sce s odd) s (.+. )/ =.. The upper quartle s (.7+.8)/ =.75. Therefore, IQR =.75 -. =.65. No-ED: meda = (.5+.7)/ =.6. The lower quartle (meda of the lower 5 observatos) s.3; the upper quartle (meda of the upper half of the data) s 7.9. Therefore, IQR = 7.9 -.3 = 7.6. b. ED: mld outlers are less tha. -.5(.65) = -3.875 or greater tha.75 +.5(.65) = 6.75. Etreme outlers are less tha. - 3(.65) = -7.85 or greater tha.75 + 3(.65) =.7. So, the two largest observatos (.7,.) are etreme outlers ad the et two largest values (8.9, 9.) are mld outlers. There are o outlers at the lower ed of the data. No-ED: mld outlers are less tha.3 -.5(7.6) = -. or greater tha 7.9 +.5(7.6) = 9.3. Note that there are o mld outlers the data, hece there ca ot be ay etreme outlers ether.
c. A comparatve boplot appears below. The outlers the ED data are clearly vsble. There s otceable postve skewess both samples; the No-Ed data has more varablty the the Ed data; the typcal values of the ED data ted to be smaller tha those for the No-ED data. No-ED ED Cocetrato (mg/l) 79. a. [ ( ), so ] b. s ( ) s ( ) ( ) ( ) ( ) Whe the epresso for from a s substtuted, the epresso braces smplfes to the followg, as desred: ( ( ) ) 5(.58).8.5 6 6 ( ) 4 (.8.58) s s.5. 45.38. 38 ( ) 5 (6) c.. 53 So the stadard devato s.38. 53.