Test bank and solution manual of ch02 frequency distributions and graphs (1)

Chapter - Frequency Distributions and Graphs EXERCISE SET 2-1 continued Width œ 31 ƒ œ 6.2 or Frequency distributions are used to organize data in a meaningful way, to facilitate computational procedures for statistics, to make it easier to draw charts and graphs, and to make comparisons among different sets of data Limits 21 - 27 28 - 34 35 - 41 42 - 48 49 - 55 Categorical distributions are used with nominal or ordinal data, ungrouped distributions are used with data having a small range, and grouped distributions are used when the range of the data is large Less than 20.5 Less than 27.5 Less than 34.5 Less than 41.5 Less than 48.5 Less than 55.5 a 31.5  38.5ß $# # $) œ (! # œ 35ß 38.5  31.5 œ ( b 85.5  104.5ß )' # "!% œ "*! # œ 95ß 104.5  85.5 œ "* c 894.5  905.5ß )*& # *!& œ ")!! # œ 900ß 905.5  894.5 œ "" d 12.25  13.55ß "#ị$ # "$ị& #&ị) # 12.9ò 13.55 12.25 1.3 e 3.175 4.965ò $ị") # %ị*' )ị"% # 4.07ò 4.965 3.175 1.79 Limits 165 - 185 186 - 206 207 - 227 228 - 248 249 - 269 270 - 290 291 - 311 312 - 332 a Class width is not uniform b Class limits overlap, and class width is not uniform c A class has been omitted d Class width is not uniform Tally f 10% M 28 70% H 15% S 40 5% 100% Boundaries 164.5 - 185.5 185.5 - 206.5 206.5 - 227.5 227.5 - 248.5 248.5 - 269.5 269.5 - 290.5 290.5 - 311.5 311.5 - 332.5 Less than 164.5 Less than 185.5 Less than 206.5 Less than 227.5 Less than 248.5 Less than 269.5 Less than 290.5 Less than 311.5 Less than 332.5 Percent A cf 15 20 27 30 f 15 13 1 50 A peak occurs in class 207 - 227 There are no empty classes Each of the three highest classes has one data value An open-ended frequency distribution has either a first class with no lower limit or a last class with no upper limit They are necessary to accomodate all the data Class f 30 H œ 325 L œ 165 Range œ 325  165 œ 160 Width œ 160 ƒ œ 20 round up to 21 Five to twenty classes Width should be an odd number so that the midpoint will have the same place value as the data Boundaries 20.5 - 27.5 27.5 - 34.5 34.5 - 41.5 41.5 - 48.5 48.5 - 55.5 cf 10 25 38 47 48 49 50 10 H œ 110 L œ 54 Range œ 110  54 œ 56 Width œ 56 ƒ œ round up to H œ 52 L œ 21 Range œ 52  21 œ 31 Chapter - Frequency Distributions and Graphs 10 continued Limits Boundaries 54 - 62 53.5 - 62.5 63 - 71 62.5 - 71.5 72 - 80 71.5 - 80.5 81 - 89 80.5 - 89.5 90 - 98 89.5 - 98.5 99 - 107 98.5 - 107.5 108 - 116 107.5 - 116.5 Less than 53.5 Less than 62.5 Less than 71.5 Less than 80.5 Less than 89.5 Less than 98.5 Less than 107.5 Less than 116.5 12 continued Limits 5427 - 17,733 17,734 - 30,040 30,041 - 42,347 42,348 - 54,654 54,655 - 66,961 66,962 - 79,268 79,269 - 91,575 f 30 Boundaries 745.5 - 752.5 752.5 - 759.5 759.5 - 766.5 766.5 - 773.5 773.5 - 780.5 Less than 745.5 Less than 752.5 Less than 759.5 Less than 766.5 Less than 773.5 Less than 780.5 f 17 1 1 25 The majority of the data values are in the lowest class There are no empty classes in the distribution cf 13 21 25 26 29 30 cf 17 18 19 20 21 22 25 Less than 5426.5 Less than 17,733.5 Less than 30,040.5 Less than 42,347.5 Less than 54,654.5 Less than 66,961.5 Less than 79,268.5 Less than 91,575.5 11 H œ 780 L œ 746 Range œ 780  746 œ 34 Width œ 34 ƒ œ 6.8 round up to Limits 746 - 752 753 - 759 760 - 766 767 - 773 774 - 780 Boundaries 5426.5 - 17,733.5 17,733.5 - 30,040.5 30,040.5 - 42,347.5 42,347.5 - 54,654.5 54,654.5 - 66,961.5 66,961.5 - 79,268.5 79,268.5 - 91,575.5 13 H œ 70 L œ 27 Range œ 70  27 œ 43 Width œ 43 ƒ œ 6.1 or f 30 Limits 27 - 33 34 - 40 41 - 47 48 - 54 55 - 61 62 - 68 69 - 75 cf 10 18 27 30 Boundaries f 26.5 - 33.5 33.5 - 40.5 14 40.5 - 47.5 15 47.5 - 54.5 11 54.5 - 61.5 61.5 - 68.5 68.5 - 75.5 55 Less than 26.5 Less than 33.5 Less than 40.5 Less than 47.5 Less than 54.5 Less than 61.5 Less than 68.5 Less than 75.5 12 H œ 91,570 L œ 5427 Range œ 91,570  5427 œ 86,143 Width œ 86,143 ƒ œ 12,306.1 Round up to 12,307 cf 21 36 47 50 53 55 14 H œ 51.7 L œ 1.2 Range œ 51.7  1.2 œ 50.5 Width œ 50.5 ƒ œ 10.1 round up to 11 Chapter - Frequency Distributions and Graphs 14 continued Limits Boundaries - 10 -0.5 - 10.5 11 - 21 10.5 - 21.5 22 - 32 21.5 - 32.5 33 - 43 32.5 - 43.5 44 - 54 43.5 - 54.5 Less than -0.5 Less than 10.5 Less than 21.5 Less than 32.5 Less than 43.5 Less than 54.5 16 continued Limits Boundaries 140 - 230 139.5 - 230.5 231 - 321 230.5 - 321.5 322 - 412 321.5 - 412.5 413 - 503 412.5 - 503.5 504 - 594 503.5 - 594.5 595 - 685 594.5 - 685.5 686 - 776 685.5 - 776.5 777 - 867 776.5 - 867.5 f 16 cf 13 15 15 16 Less than 139.5 Less than 230.5 Less than 321.5 Less than 412.5 Less than 503.5 Less than 594.5 Less than 685.5 Less than 776.5 Less than 867.5 15 H œ 635 L œ Width œ 635  œ 629 Range œ 629 ƒ œ 125.8 round up to 127 Limits - 132 133 - 259 260 - 386 387 - 513 514 - 640 Boundaries 5.5 - 132.5 132.5 - 259.5 259.5 - 386.5 386.5 - 513.5 513.5 - 640.5 f 16 0 20 cf 11 16 20 24 28 29 29 30 17 H œ 123 L œ 77 Range œ 123  77 œ 46 Width œ 46 ƒ œ 6.6 or Limits 77 - 83 84 - 90 91 - 97 98 - 104 105 - 111 112 - 118 119 - 125 The greatest concentration of data values is in the lowest class All but one of the data values are in the lowest two classes There is one extremely large data value occurring in the highest class Less than 5.5 Less than 132.5 Less than 259.5 Less than 386.5 Less than 513.5 Less than 640.5 f 11 4 1 30 cf 16 19 19 19 20 Boundaries 76.5 - 83.5 83.5- 90.5 90.5- 97.5 97.5- 104.5 104.5 - 111.5 111.5 - 118.5 118.5 - 125.5 Less than 76.5 Less than 83.5 Less than 90.5 Less than 97.5 Less than 104.5 Less than 111.5 Less than 118.5 Less than 125.5 16 H œ 857 L œ 140 Width œ 857  140 œ 717 Range œ 717 ƒ œ 89.6 or 91 cf 22 30 31 32 18 H œ 31.5 L œ 7.5 Range œ 31.5  7.5 œ 24 Width œ 24 ƒ œ 4.8 or 5 f 1 14 1 32 Chapter - Frequency Distributions and Graphs 18 continued Limits Boundaries 7.5 - 12.4 7.45 - 12.45 12.5 - 17.4 12.45 - 17.45 17.5 - 22.4 17.45 - 22.45 22.5 - 27.4 22.45 - 27.45 27.5 - 32.4 27.45 - 32.45 f 10 25 Limits 70 - 116 117 - 163 164 - 210 211 - 257 258 - 304 305 - 351 352 - 398 cf 15 21 25 Less than 7.45 Less than 12.45 Less than 17.45 Less than 22.45 Less than 27.45 Less than 32.45 Boundaries 69.5 - 116.5 116.5 - 163.5 163.5 - 210.5 210.5 - 257.5 257.5 - 304.5 304.5 - 351.5 351.5 - 398.5 cf 14 20 26 26 27 28 Less than 69.5 Less than 116.5 Less than 163.5 Less than 210.5 Less than 257.5 Less than 304.5 Less than 351.5 Less than 398.5 19 The percents add up to 101% They should total 100% unless rounding was used f 6 1 28 EXERCISE SET 2-2 10 frequency 50 40 30 20 10 69.5-116.5 116.5-163.5 163.5-210.5 210.5-257.5 257.5-304.5 304.5-351.5 351.5-398.5 89.598.5 98.5107.5 107.5116.5 116.5125.5 125.5134.5 Number of faculty I.Q 10 frequency frequency 60 40 20 85 94 103 112 121 130 139 93 I.Q 140 187 234 281 328 375 120 100 80 60 40 20 89.5 98.5 107.5 116.5 125.5 cumulative frequency cumulative frequency Number of faculty 134.5 I.Q 30 25 20 15 10 69.5 116.5 163.5 210.5 257.5 304.5 351.5 398.5 Number of faculty Eighty applicants not need to enroll in the summer programs "# #) œ 0.429 or 42.9% have 180 or more The histogram and frequency polygon are positively skewed Chapter - Frequency Distributions and Graphs Boundaries 2.5 - 45.5 45.5 - 88.5 88.5 - 131.5 131.5 - 174.5 174.5 - 217.5 217.5 - 260.5 f 19 19 10 1 50 14 12 10 frequency Limits - 45 46 - 88 89 - 131 132 - 174 175 - 217 218 - 260 39.85-42.85 42.85-45.85 45.85-48.85 48.85-51.85 51.85-54.85 54.85-57.85 M illions of Dolla rs 14 cf 19 38 48 49 49 50 10 frequency Less than 2.5 Less than 45.5 Less than 88.5 Less than 131.5 Less than 174.5 Less than 217.5 Less than 260.5 12 38.35 41.35 44.35 47.35 50.35 53.35 56.35 59.35 Millions of Dollars cumulative frequency 35 20 frequency 15 10 30 25 20 15 10 38.85 2.5-45.5 45.5-88.5 42.85 45.85 48.85 51.85 54.85 57.85 Millions of Dollars 88.5-131.5 131.5-174.5 174.5-217.5 217.5-260.5 Counties, parishes, or divisions The distribution is left skewed or negatively skewed The distribution is positively skewed frequency 20 Limits - 43 44 - 86 87 - 129 130 - 172 173 - 215 216 - 258 259 - 301 302 - 344 15 10 24 67 110 153 196 239 cumulative frequency Counties, parishes, or divisions 60 50 Boundaries 0.5 - 43.5 43.5 - 86.5 86.5 - 129.5 129.5 - 172.5 172.5 - 215.5 215.5 - 258.5 258.5 - 301.5 301.5 - 344.5 40 f 24 17 0 50 30 20 10 Less than 0.5 Less than 43.5 Less than 86.5 Less than 129.5 Less than 172.5 Less than 215.5 Less than 258.5 Less than 301.5 Less than 344.5 2.5 45.5 88.5 131.5 174.5 217.5 260.5 Counties, parishes, or divisions cf 24 41 44 48 49 49 49 50 The distribution is positively skewed Chapter - Frequency Distributions and Graphs continued continued 30 20 20 Frequency Frequency 25 15 10 0.5-43.5 43.5-86.5 86.5-129.5 15 10 129.5-172.5 172.5-215.5 215.5-258.5 258.5-301.5 301.5-344.5 Accidents 5.5-8.5 8.5-11.5 11.5-14.5 14.5-17.5 17.5-20.5 20.5-23.5 23.5-26.5 30 Costs of utilities Frequency 25 20 15 20 Frequency 10 22 65 108 151 194 237 280 323 Accide nts 15 10 10 13 16 19 22 25 Costs of utilities 60 50 40 30 Cumulative frequency Cumulative Frequency 20 10 0.5 43.5 86.5 129.5 172.5 215.5 258.5 301.5 344.5 Accide nts Limits 6-8 - 11 12 - 14 15 - 17 18 - 20 21 - 23 24 - 26 35 30 25 20 15 10 5.5 8.5 11.5 14.5 17.5 20.5 23.5 26.5 Costs of utilities Boundaries f 5.5 - 8.5 12 8.5 - 11.5 16 11.5 - 14.5 14.5 - 17.5 17.5 - 20.5 20.5 - 23.5 23.5 - 26.5 33 Less than 5.5 Less than 8.5 Less than 11.5 Less than 14.5 Less than 17.5 Less than 20.5 Less than 23.5 Less than 26.5 Limits - 22 23 - 45 46 - 68 69 - 91 92 - 114 115 - 137 138 - 160 cf 12 28 31 32 32 32 33 The distribution is positively skewed Boundaries -0.5 - 22.5 22.5 - 45.5 45.5 - 68.5 68.5 - 91.5 91.5 - 114.5 114.5 - 137.5 137.5 - 160.5 f (1998) 18 1 0 30 f (2003) 26 1 1 30 Chapter - Frequency Distributions and Graphs continued Limits 83.1 - 90.0 90.1 - 97.0 97.1 - 104.0 104.1 - 111.0 111.1 - 118.0 118.1 - 125.0 frequency 20 15 10 -0.522.5 22.545.5 45.568.5 68.591.5 91.5114.5 114.5137.5 137.5160.5 frequency Days 1998 30 25 20 15 10 -0.522.5 22.545.5 45.568.5 68.591.5 91.5114.5 114.5137.5 Boundaries 83.05 - 90.05 90.05 - 97.05 97.05 - 104.05 104.05 - 111.05 111.05 - 118.05 118.05 - 125.05 Less than 83.05 Less than 90.05 Less than 97.05 Less than 104.05 Less than 111.05 Less than 118.05 Less than 125.05 137.5160.5 Days 2003 Both distributions are positively skewed, but the data are somewhat more spread out in the first three classes in 1998 than in 2003 There are two large data values in the 2003 data f 25 cf 14 21 24 25 frequency 83.0590.05 90.0597.05 97.05104.05 104.05111.05 111.05118.05 118.05125.05 Scores 12 10 8 2.252.95 2.953.65 3.654.35 4.355.05 5.055.75 frequency frequency 5.756.45 Tim e 86.55 93.55 100.55 107.55 114.55 121.55 Scores 10 30 frequency frequency 15 1.9 2.6 3.3 4.0 4.7 5.4 6.1 6.8 Tim e 20 10 90.05 97.05 104.05 111.05 118.05 125.05 Scores 40 30 20 10 10 2.25 2.95 3.65 4.35 5.05 5.75 20 6.45 frequency cumulative frequency 83.05 50 Tim e The data values fall somewhat on the left side of the distribution The histogram is right skewed There are no gaps in the histogram 15 10 17.5 22.5 22.5 27.5 27.5 32.5 32.5 37.5 37.5 42.5 % At or Above Reading Level 42.5 47.5 Chapter - Frequency Distributions and Graphs 10 continued 11 continued 12 10 15 Frequency frequency 20 10 0 17.5 22.5 22.5 27.5 27.5 32.5 32.5 37.5 37.5 42.5 42.5 47.5 139.5230.5 230.5321.5 321.5412.5 412.5503.5 % At or Above Math Level 503.5594.5 594.5685.5 685.5776.5 776.5867.5 Unclaimed prizes The distribution of math percentages is more bell-shaped than the distribution of reading percentages, and its peak in the class of 32.5  37.5 is not as high as the peak of the reading percentages 12 Frequency 10 185 Less than 139.5 Less than 230.5 Less than 321.5 Less than 412.5 Less than 503.5 Less than 594.5 Less than 685.5 Less than 776.5 Less than 867.5 f 11 4 1 30 367 458 549 640 731 822 35 Cumulative frequency Boundaries 139.5 - 230.5 230.5 - 321.5 321.5 - 412.5 412.5 - 503.5 503.5 - 594.5 594.5 - 685.5 685.5 - 776.5 776.5 - 867.5 276 Unclaimed prizes 30 25 20 15 10 139.5 230.5 321.5 412.5 503.5 594.5 685.5 776.5 867.5 Unclaimed prizes 12 cf 11 16 20 24 28 29 29 30 12 10 Frequency 11 Limits 140 - 230 231 - 321 322 - 412 413 - 503 504 - 594 595 - 685 686 - 776 777 - 867 7.45-12.45 12.45-17.45 17.45-22.45 22.45-27.45 27.45-32.45 State Gasoline Tax The histogram shows that state gasoline taxes are somewhat normal with the peak in the middle of the graph The distribution is positively skewed relative frequency 13 0.4 0.3 0.2 0.1 89.598.5 98.5107.5 107.5116.5 I Q 10 116.5125.5 125.5134.5 Chapter - Frequency Distributions and Graphs 14 continued 0.4 0.6 0.3 0.5 Frequency relative frequency 13 continued 0.2 0.1 85 94 103 112 121 130 0.4 0.3 0.2 0.1 139 I Q 0.5-43.5 43.5-86.5 86.5-129.5 129.5-172.5 172.5-215.5 215.5-258.5 258.5-301.5 301.5-344.5 0.8 0.6 0.6 0.5 Frequency cumulative relative frequency Accidents 0.4 0.2 89.5 98.5 107.5 116.5 125.5 134.5 0.4 0.3 0.2 0.1 I Q 22 65 108 151 194 237 280 323 258.5 301.5 Accidents 14 Limits - 43 44 - 86 87 - 129 130 - 172 173 - 215 216 - 258 259 - 301 302 - 344 Boundaries 0.5 - 43.5 43.5 - 86.5 86.5 - 129.5 129.5 - 172.5 172.5 - 215.5 215.5 - 258.5 258.5 - 301.5 301.5 - 344.5 Less than 0.5 Less than 43.5 Less than 86.5 Less than 129.5 Less than 172.5 Less than 215.5 Less than 258.5 Less than 301.5 Less than 344.5 Cumulative frequency The proportion of applicants who need to enroll in a summer program is 0.26 or 26% rf 0.48 0.34 0.06 0.08 0.02 0 0.02 1.2 0.8 0.6 0.4 0.2 0.5 43.5 86.5 129.5 172.5 215.5 Accidents 15 H œ 270 L œ 80 Range œ 270  80 œ 190 Width œ 190 ƒ œ 27.1 or 28 Use width œ 29 (rule 2) crf 0.48 0.82 0.88 0.96 0.98 0.98 0.98 1.00 Limits 80 - 108 109 - 137 138 - 166 167 - 195 196 - 224 225 - 253 254 - 282 Boundaries 79.5 - 108.5 108.5 - 137.5 137.5 - 166.5 166.5 - 195.5 195.5 - 224.5 224.5 - 253.5 253.5 - 282.5 *due to rounding Of the states 82% have fewer than 87 accidents per year Less than 79.5 Less than 108.5 Less than 137.5 Less than 166.5 Less than 195.5 Less than 224.5 Less than 253.5 Less than 282.5 11 crf 0.00 0.17 0.45 0.49 0.69 0.91 0.95 0.99 f 13 10 2 rf 0.17 0.28 0.04 0.20 0.22 0.04 0.04 0.99* 344.5 Chapter - Frequency Distributions and Graphs 15 continued 16 continued 0.25 relative frequency relative frequency 0.3 0.2 0.15 0.1 0.05 79.5-108.5 108.5-137.5 137.5-166.5 166.5-195.5 195.5-224.5 224.5-253.5 153.5-282.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 11.5-19.5 Calories 19.5-27.5 27.5-35.5 35.5-43.5 43.5-51.5 51.5-59.5 Gram s 0.45 0.4 0.2 relative frequency relative frequency 0.3 0.25 0.15 0.1 0.05 65 94 123 152 181 210 239 268 297 0.35 0.3 0.25 0.2 0.15 0.1 0.05 Calories 15.5 23.5 31.5 39.5 47.5 55.5 63.5 Gram s 0.8 1.2 0.6 cumulative relative frequency cumulative relative frequency 7.5 1.2 0.4 0.2 79.5 108.5 137.5 166.5 195.5 224.5 253.5 282.5 Calories 0.8 0.6 0.4 0.2 11.5 19.5 27.5 35.5 43.5 51.5 Gram s The histogram has two peaks The histogram is positively skewed 16 H œ 57 L œ 12 Range œ 57  12 œ 45 Width œ 45 ƒ œ 7.5 or Limits 12 - 19 20 - 27 28 - 35 36 - 43 44 - 51 52 - 59 Boundaries f 11.5 - 19.5 19.5 - 27.5 17 27.5 - 35.5 10 35.5 - 43.5 43.5 - 51.5 51.5 - 59.5 40 Less than 11.5 Less than 19.5 Less than 27.5 Less than 35.5 Less than 43.5 Less than 51.5 Less than 59.5 17 Boundaries -0.5 - 27.5 27.5 - 55.5 55.5 - 83.5 83.5 - 111.5 111.5 - 139.5 139.5 - 167.5 167.5 - 195.5 rf 0.175 0.425 0.25 0.10 0.025 0.025 1.000 Less than -0.5 Less than 27.5 Less than 55.5 Less than 83.5 Less than 111.5 Less than 139.5 Less than 167.5 Less than 195.5 crf 0.000 0.175 0.600 0.850 0.950 0.975 1.000 12 crf 0.87 0.03 0.00 0.03 0.00 0.03 0.03 0.99 crf 0.00 0.87 0.90 0.90 0.93 0.93 0.96 0.99 59.5 Chapter - Frequency Distributions and Graphs Frequency 17 continued 18 continued Based on the histograms, the older dogs have longer reaction times Also, the reaction times for older dogs is more variable 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 -0.5-27.5 27.5-55.5 55.5-83.5 83.5-111.5 111.5-139.5 19 Limits 22 - 24 25 - 27 28 - 30 31 - 33 34 - 36 37 - 39 40 - 42 139.5-167.5 137.5-195.5 Air Quality ( Days) - 2003 Frequency 0.8 0.6 0.4 0.2 Boundaries 21.5 - 24.5 24.5 - 27.5 27.5 - 30.5 30.5 - 33.5 33.5 - 36.5 36.5 - 39.5 39.5 - 42.5 Xm 23 26 29 32 35 38 41 11 34 57 80 103 126 149 Air Quality (Days) - 2003 Frequency 0.6 0.4 0.2 27.5 55.5 83.5 111.5 139.5 167.5 195.5 Air Quality (Days) - 2003 fr e q ue ncy 18 20 fr e que ncy cf 4 10 15 18 20 Less than 21.5 Less than 24.5 Less than 27.5 Less than 30.5 Less than 33.5 Less than 36.5 Less than 39.5 Less than 42.5 0.8 -0.5 f 20 15 10 23 26 29 32 35 38 41 Seconds 2.25 - 2.95 2.95 - 3.65 3.65 - 4.35 4.35 - 5.05 5.05 - 5.75 5.75 - 6.45 Seconds fr e qu e ncy 25 20 15 10 fr e q u e n cy 20 15 10 5 21.5 24.5 27.5 30.5 33.5 36.5 39.5 42.5 2.6 3.3 4.7 5.4 6.1 Seconds fr e que n cy Seconds 20 a b 14 c 10 d 16 50 40 30 20 10 2.25 2.95 3.65 4.35 5.05 5.75 6.45 Seconds 13 Chapter - Frequency Distributions and Graphs EXERCISE SET 2-3 Calories burned per minute May June July August September October November f 18 79 101 344 459 280 61 16 14 12 10 Running Skiing Tennis Golfing Bicycling Walking 700 500 Number Number of Hurricanes 600 500 400 300 400 300 200 200 100 100 0 May June July Aug Sept Oct North America Nov Europe Asia South America Australia Africa South America f $8.7 14.2 9.3 12.7 10.0 Wendy's KFC Pizza Hut Burger King Subway North America Europe Australia Asia Africa 100 200 300 400 500 600 700 Num ber of roller coasters Sales of Fast Foods Subway Burger King Time (hours) Pizza Hut KFC Wendy's $0.00 $3.00 $6.00 $9.00 $12.00 $15.00 35 30 25 20 15 10 Time (hours) Dollars (billions) Dollars (billions) 15 10 KFC Burger King Subway Pizza Hut Wendy's Sales of Fast Foods 14 Thailand China France Thailand China France United States Brazil 35 30 25 20 15 10 United States Brazil Chapter - Frequency Distributions and Graphs Revenue (billions) 10 Personal Business Visit friends or family Work-related Leisure $15.00 $10.00 $5.00 $0.00 2001 2002 2003 2004 2005 146 330 225 299 1000 14.6% 52.56° 33.0% 118.8° 22.5% 81.0° 29.9% 107.64° 100% 360° 2006 Year Personal Leisure 14.6% 29.9% Sales of coffee are increasing V isit 33.0% Work 22.5% Major accidents About "3 of the travelers visit friends or relatives, with the fewest travelling for personal business 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 Year 11 Marital Status DivorcedNever married 4% 8% Temperature 58.2 58.1 Widow ed 31% 58 57.9 Married 57% 57.8 57.7 2004 2005 2006 2007 2008 Year After a slight increase in 2005, the average temperature has declined somewhat in the following years Educational Attainment Less than 9th grade 19% 14% 13% 9 - 12 but no diploma H.S graduate 18% 384 382 380 378 376 374 372 370 Some college 36% 2004 2005 2006 2007 12 White Silver Black Red Gray Blue Other 2008 Year The atmospheric concentration of carbon dioxide has been steadily increasing over the years 15 19% 18% 16% 13% 12% 12% 10% 68.4° 64.8° 57.6° 46.8° 43.2° 43.2° 36.0° Bachelor's/advanced degree Chapter - Frequency Distributions and Graphs 12 continued Other 10% Blue 12% Gray 12% Red 13% 13 Career change New job Start business Retire 34% 29% 21% 16% 100% 15 4 5 6 Popular Vehicle Colors White 19% Silver 18% Black 16% 9 6 4 7 7 The distribution is somewhat symmetric and unimodal The majority of the Presidents were in their 50's when inaugurated 16 10 11 12 13 14 15 16 17 18 19 122.4° 104.4° 75.6° 57.6° 360.0° Pie chart: Retire 16.0% 5 Career change 34.0% Start business 21.0% 0 ! ! ! ! 0 0 ! ! 0 0 0 0 0 0 0 0 5 17 Variety New job 29.0% * * ) & Variety * ) $ $ ) $ # $ & $ " # ! # " ! " # $ % & ' $ & ' " ! # ) ) # & $ & # & & ' ( * The distributions are similar but variety seems to be more variable than variety Pareto chart: 40% 18 35% 30% Math 25% 9 20% 15% 3 Reading 2 10% 1 0 6 6 5% 0% Career change New job Start business 19 Answers will vary Retire 20 The pie graph better represents the data since we are looking at parts of a whole 40 30 14 a Time series graph b Pie graph c Pareto chart d Pie graph e Time series graph f Pareto chart U S 20 Japan 10 1993 1994 1995 1996 1997 16 7 Chapter - Frequency Distributions and Graphs 20 continued The United States has many more launches than Japan The number of launches is relatively stable for Japan, while launches varied more for the U S The U S launches decreased slightly in 1995 and increased after that year The two variables used are the independent variable, B, and the dependent variable, C Two variables are positively related when the dependent variable, C, increases as the independent variable, B, increases The points on the scatter plot fall approximately in an ascending straight line 21 1500 1000 Two variables are negatively related when the dependent variable, C, decreases as the independent variable, B, increases The points on the scatter plot fall approximately in a descending straight line Veal Lamb 500 1950 1960 1970 1980 1990 In 1950, veal production was considerably higher than lamb By 1970, production was approximately the same for both 70 60 Stories 50 22 40 30 10 0 400 300 200 100 200 400 600 800 1000 Height d N or th w U es S t A irw ay s C on ti n en ta So l ut hw Br e it is st h Ai rw Am ay er s ic an Lu Ea fth gl an e sa (G er ) There appears to be a positive linear relationship between the height of a building and the number of stories in the building D el ta ni te U Am er ic an Number of Aircraft 20 800 700 600 500 A Pareto chart is most appropriate 23 Hours 20 40 60 80 Age Ita Au l y st li a an Sw y ed en Fr an Sw ce i tz er la nd D en m ar k Au st ria Be lg iu m gd o G Ki n er m m te d U ni te d U ni St at es Number of Winners 90 80 70 60 50 40 30 20 10 There appears to be a negative linear relationship between age and the number of hours spent jogging per week 24 The bottle for 2004 is much wider, giving a distorted view of the difference since only the heights of the bottles should be compared Am ou nt Spe nt o n Re cr e atio n 25 The values on the C axis start at 3.5 Also there are no data values shown for the years 2004 through 2011 210 180 150 120 90 60 30 700 800 900 1000 1100 1200 1300 Monthly Income EXERCISE SET 2-4 Scatter plot or scatter diagram 17 Chapter - Frequency Distributions and Graphs continued There appears to be a positive linear relationship between monthly income and amount spent on recreation 11 continued There appears to be neither a positive nor negative linear relationship between the number of tournaments and the earnings of LPGA golfers 12 15 Nu m b e r o f Po in ts Days M is s e d 10 0 10 20 30 40 50 60 70 Age There appears to be a positive linear relationship between an employee's age and number of days missed per year 20 10 0 There appears to be a positive linear relationship between number of wins and points scored by NHL teams 13 90 Fin al Gr ad e 80 70 60 70 80 90 100 Final Exam - STAT 101 100 90 80 70 60 There appears to be a positive linear realationship between a student's final exam score in STAT 101 and STAT 102 10 15 Num be r of Abs e nce s There appears to be a negative linear relationship between the number of absences and at student's final grade in a course 10 Num be r o f Accid e n ts 15 100 60 9000 8000 7000 14 6000 5000 4000 80 15 16 17 18 19 20 21 70 22 60 Excise Tax Ag e There appears to be a negative linear relationship between the age of a driver and the number of accidents per year 50 40 30 20 10 0 11 0.5 1.5 2.5 Average Price 1000 Ear ning s 10 Num be r of Wins Fin al Exam - ST AT 102 30 There appears to be a positive linear relationship between average price per pack of cigarettes and state excise tax 750 500 250 15 20 25 30 35 Num be r of Tournam e nts 18 Chapter - Frequency Distributions and Graphs REVIEW EXERCISES - CHAPTER Class Newspaper Television Radio Internet Class 11 12 13 14 15 16 17 18 19 20 21 22 f 10 16 12 12 50 How People Receive News Internet 24% New spaper 20% f 2 2 2 1 20 cf 10 14 16 18 19 19 20 less than 10.5 less than 11.5 less than 12.5 less than 13.5 less than 14.5 less than 15.5 less than 16.5 less than 17.5 less than 18.5 less than 19.5 less than 20.5 less than 21.5 less than 22.5 Radio 24% Television 32% 3.5 f 5 25 1.5 0.5 21.5-22.5 20.5-21.5 19.5-20.5 18.5-19.5 17.5-18.5 16.5-17.5 15.5-16.5 14.5-15.5 13.5-14.5 12.5-13.5 11.5-12.5 10.5-11.5 Class Baseballs Golf balls Tennis balls Soccer balls Footballs frequency 2.5 B.U.N Count 22 20 18 16 14 golf balls 20% 12 10 B U N Count tennis balls 24% 20 10 22.5 20.5 18.5 16.5 14.5 10.5 More tennis balls were sold than any other type of ball 15 12.5 soccer balls 20% baseballs 16% cumulative frequency footballs 20% frequency B U N Count The distribution is somewhat uniform, with a slight peak in the 16.5 - 17.5 class There is a gap in the 20.5 - 21.5 class 19 Chapter - Frequency Distributions and Graphs 10 fr e q u e n cy Boundaries f 14.5 - 19.5 19.5 - 24.5 18 24.5 - 29.5 18 29.5 - 34.5 34.5 - 39.5 50 10 188.5 207.5 226.5 245.5 264.5 283.5 302.5 321.5 Millions of Dollars cf 21 39 47 50 Less than 14.5 Less than 19.5 Less than 24.5 Less than 29.5 Less than 34.5 Less than 39.5 15 169.5 - 188.5 - 207.5 - 226.5 - 245.5 - 264.5 - 283.5 - 302.5 - 15 fr e qu e n cy Limits 15 - 19 20 - 24 25 - 29 30 - 34 35 - 39 10 179 198 217 236 255 274 293 312 Millions of Dollars 20 40 fr e q u e ncy 15 10 14.5-19.5 19.5-24.5 24.5-29.5 29.5-34.5 30 20 10 34.5-39.5 169.5 188.5 207.5 226.5 245.5 264.5 283.5 302.5 321.5 Percent completing years of college Millions of Dollars frequency 20 The typical value of the franchises is between $169.5 - $188.5 million All but one of the franchises are valued between $169.5 and $245.5 million 15 10 17 22 27 32 37 11 Limits 51 - 59 60 - 68 69 - 77 78 - 86 87 - 95 96 - 104 cumulative frequency Percent completing years of college 60 40 20 14.5 19.5 24.5 29.5 34.5 39.5 Percent completing years of college Limits 170 - 188 189 - 207 208 - 226 227 - 245 246 - 264 265 - 283 284 - 302 303 - 321 Boundaries 169.5 - 188.5 188.5 - 207.5 207.5 - 226.5 226.5 - 245.5 245.5 - 264.5 264.5 - 283.5 283.5 - 302.5 302.5 - 321.5 f 11 0 30 less than 169.5 less than 188.5 less than 207.5 less than 226.5 less than 245.5 less than 264.5 less than 283.5 less than 302.5 less than 321.5 Boundaries 50.5 - 59.5 59.5 - 68.5 68.5 - 77.5 77.5 - 86.5 86.5 - 95.5 95.5 - 104.5 Less than 50.5 Less than 59.5 Less than 68.5 Less than 77.5 Less than 86.5 Less than 95.5 Less than 104.5 cf 11 20 24 29 29 29 29 30 20 rf 0.125 0.300 0.275 0.200 0.050 0.050 1.000 crf 0.000 0.125 0.425 0.700 0.900 0.950 1.000 Chapter - Frequency Distributions and Graphs relative frequency 11 continued 13 0.4 Smoke 0.3 0.2 Experience road rage 0.1 Eat a meal 50.5-59.5 59.5-68.5 68.5-77.5 77.5-86.5 86.5-95.5 95.5-104.5 Talk on cell phone Age relative frequency Drink beverage 0% 0.4 20% 40% 60% 80% 100% 0.3 0.2 100% 0.1 80% 55 64 73 82 91 100 60% Age cumulative relative frequency 40% 1.5 20% 0% 0.5 Drink beverage 50.5 59.5 68.5 77.5 86.5 95.5 Talk on cell phone Eat a meal Experience road rage Smoke 104.5 Age 14 20 15 Days re la tive fre que ncy 12 0.4 10 0.3 0.2 2005 2006 2007 2008 Year 0.1 169.5 - 188.5 - 207.5 - 226.5 - 245.5 - 264.5 - 283.5 - 302.5 - 188.5 207.5 226.5 245.5 264.5 283.5 302.5 321.5 15 Millions of Dollars 100 0.4 Failures r e lative fr e qu e n cy 120 0.3 0.2 60 40 20 0.1 0 179 198 217 234 255 274 193 01 312 02 03 04 05 06 07 08 09 Year Millions of Dollars cu m u lative r e lative fr e q ue ncy 80 Bank failures increased in 2002 from to 11, then dropped until 2008, when they increased to 28 The year 2009 brought an increase to 98 1.5 0.5 169.5 188.5 207.5 226.5 245.5 264.5 283.5 302.5 321.5 Millions of Dollars 21 Chapter - Frequency Distributions and Graphs Amount (billions) 16 20 14000 12000 10000 8000 6000 4000 2000 03 04 05 06 07 08 09 Year 21 10 11 12 13 14 15 16 17 18 19 20 21 Amount (troy ounces) 17 2000 1500 1000 500 2003 2004 2005 2006 2007 2008 Year There has been a steady increase in the amount of gold produced by Columbia over the recent years 22 20 21 22 23 24 25 26 18 Spendingof College Freshmen Shoes 6% Clothing 11% DormItems 27% 1 2 Electronics 56% 3 5 2 6 0 1 7 8 8 9 3 7 8 8 The distribution of aptitude scores is fairly uniform Ratin gs of Pr og r am s 23 19 Undecided 8% No 26% 20 15 10 0 10 20 30 N o o f v ie w e r s ( in m illio n s ) Yes 66% There appears to be a positive linear relationship between the number of viewers (in millions) and the ratings of 15 television programs The majority of people surveyed would like to spend the rest of their careers with their present employer 22 Chapter - Frequency Distributions and Graphs 20 Final Gr ade 24 Class 0.5  1.5 1.5  2.5 2.5  3.5 3.5  4.5 4.5  5.5 5.5  6.5 6.5  7.5 7.5  8.5 8.5  9.5 95 90 85 80 75 70 2.5 7.5 10 12.5 15 Nu m b e r o f Ho u r s There appears to be a positive linear relationship between the final grade a student receives and the number of hours of tutoring received by the student f 30 cf 13 15 21 23 26 30 less than 0.5 less than 1.5 less than 2.5 less than 3.5 less than 4.5 less than 5.5 less than 6.5 less than 7.5 less than 8.5 less than 9.5 CHAPTER QUIZ False False False True True False False c c 10 b 11 b 12 Categorical, ungrouped, grouped 13 5, 20 14 Categorical 15 Time series 16 Stem and leaf plot 17 Vertical or y 18 Class f cf H 6 A 11 M 17 C 25 25 21 Number 2 Item s Purchased Number 0 10 Items Purchased 19 Mobile Home 24% House 24% Number Condominium 32% Apartment 20% 30 25 20 15 10 0.5 1.5 2.5 3.5 4.5 5.5 6.5 Items Purchased 23 7.5 8.5 9.5 Chapter - Frequency Distributions and Graphs 24 Boundaries 26.5 - 90.5 90.5 - 154.5 154.5 - 218.5 218.5 - 282.5 282.5 - 346.5 346.5 - 410.5 410.5 - 474.5 474.5 - 538.5 538.5 - 602.5 f 13 2 25 400 300 To ns 22 Limits 27 - 90 91 - 154 155 - 218 219 - 282 283 - 346 347 - 410 411 - 474 475 - 538 539 - 602 200 100 Paper Type of Waste 14 12 10 Plastics Glass Yard Waste Aluminum Iron/steel Paper 100 200 Number of Murders 300 25 Other 12% 14 12 10 Identity Thefts Phishing 5% Computer checks 9% Lost or stolen item 45% Stolen mail 11% Retail purchases 18% 58.5 122.5 186.5 250.5 314.5 378.5 442.5 506.5 570.5 Number of Murders 30 25 26 20 15 4000 Number of deaths 10 26.5 400 Tons The distribution is positively skewed with one more than half of the data values in the lowest class frequency Glass Plastics 26.5 - 90.5 - 154.5 - 218.5 - 282.5 - 346.5 - 410.5 - 474.5 - 538.5 90.5 154.5 218.5 282.5 346.5 410.5 474.5 538.5 602.5 cumulative frequency Yard waste 23 frequency Iron/Steel Aluminum 90.5 154.5 218.5 282.5 346.5 410.5 474.5 538.5 602.5 Number of Murders 3000 2000 1000 2020 2025 2030 Year 24 2035 Chapter - Frequency Distributions and Graphs 27 1 6 3 8 8 9 28 Sale s 250 200 150 100 50 0 100 200 300 400 M ile s Tr ave le d There appears to be a positive linear relationship between the number of miles traveled and the sales (in hundreds of dollars) of a sales representative 25 ... Hut Wendy's Sales of Fast Foods 14 Thailand China France Thailand China France United States Brazil 35 30 25 20 15 10 United States Brazil Chapter - Frequency Distributions and Graphs Revenue (billions)... between average price per pack of cigarettes and state excise tax 750 500 250 15 20 25 30 35 Num be r of Tournam e nts 18 Chapter - Frequency Distributions and Graphs REVIEW EXERCISES - CHAPTER... distribution of math percentages is more bell-shaped than the distribution of reading percentages, and its peak in the class of 32.5  37.5 is not as high as the peak of the reading percentages 12 Frequency