Solution manual CH02 frequency distributions andgraphs

Chapter - Frequency Distributions and Graphs H œ 36 L œ Range œ 36  œ 29 Width œ 29 ƒ œ 4.83 or EXERCISE SET 2-2 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 - 11 12 - 16 17 - 21 22 - 26 27 - 31 32 - 36 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 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 f 10% M 28 70% H 15% S 40 5% 100% Boundaries 163.5 - 1306.5 1306.5 - 2449.5 2449.5 - 3592.5 3592.5 - 4735.5 4735.5 - 5878.5 5878.5 - 7021.5 7021.5 - 8164.5 8164.5 - 9307.5 9307.5 - 10450.5 10450.5 - 11593.5 f 25 12 5 0 1 50 The majority of the data is clustered in the first two classes Percent A Limits 19 - 21 22 - 24 25 - 27 28 - 30 31 - 33 Limits 164 - 1306 1307 - 2449 2450 - 3592 3593 - 4735 4736 - 5878 5879 - 7021 7022 - 8164 8165 - 9307 9308 - 10450 10451 - 11593 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 cf 16 18 18 19 10 H œ 11,588 L œ 164 Range œ 11,588  164 œ 11,424 Width œ 11,424 ƒ 10 œ 1142.4 Width œ 1143 Five to twenty classes Width should be an odd number so that the midpoint will have the same place value as the data Class f 19 Boundaries f cf 18.5 - 21.5 2 21.5 - 24.5 13 15 24.5 - 27.5 11 26 27.5 - 30.5 29 30.5 - 33.5 30 30 The average speed is about 24.5 mph a ""ị& ")ị&ò "#") $! # # "&ò ")ị& ""ị& ( b &&ị& (%ị&ò &'(% "$! # # '&ò (%ị& &&ị& "* c '*%ị& (!&ị&ò '*&(!& "%!! # # (!!ò (!&ị& '*%ị& "" d "$ị&& "%ị(&ò "$ị'"%ị( #)ị$ # # "%ị"&ò "%ị(& "$ị&& "ị# e #ị"%& $ị*$&ò #ị"&$ị*$ 'ị!) # # $ị!%ò $ị*$& #ị"%& "Þ(* Boundaries 6.5 - 11.5 11.5 - 16.5 16.5 - 21.5 21.5 - 26.5 26.5 - 31.5 31.5 - 36.5 11 H œ 780 L œ 746 Range œ 780  746 œ 34 Width œ 34 ƒ œ 5.' or 6; round up to cf 25 37 42 47 48 48 48 49 49 50 Chapter - Frequency Distributions and Graphs 11 continued Limits Boundaries 745 - 751 744.5 - 751.5 752 - 758 751.5 - 758.5 759 - 765 758.5 - 765.5 766 - 772 765.5 - 772.5 773 - 779 772.5 - 779.5 780 - 786 779.5 - 786.5 15 f 11 30 cf 16 27 29 30 12 H œ 93 L œ Range œ 93  œ 93 Width œ 93 ƒ ¸ 13.29 or 14 Use w œ 15 for odd number Limits - 14 15 - 29 30 - 44 45 - 59 60 - 74 75 - 89 90 - 104 Boundaries -0.5 - 14.5 14.5 - 29.5 29.5 - 44.5 44.5 - 59.5 59.5 - 74.5 74.5 - 89.5 89.5 - 104.5 f 14 10 1 33 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 Limits - 101 102 - 198 199 - 295 296 - 392 393 - 489 490 - 586 587 - 683 684 - 780 cf 14 24 28 29 30 32 33 cf 14 26 39 44 47 Boundaries 4.5 - 101.5 101.5 - 198.5 198.5 - 295.5 295.5 - 392.5 392.5 - 489.5 489.5 - 586.5 586.5 - 683.5 683.5 - 780.5 f 17 6 2 39 cf 17 23 29 31 33 36 37 39 17 H œ 11,413 L œ 150 Range œ 11,413  150 œ 11,263 Width œ 11,263 ƒ 10 œ 1126.3 or 1127 cf 21 36 47 50 53 55 Limits 150 - 1276 1277 - 2403 2404 - 3530 3531 - 4657 4658 - 5784 5785 - 6911 6912 - 8038 8039 - 9165 9166 - 10,292 10,293 - 11,419 14 H œ 4040 L œ 70 Range œ 4040  70 œ 3970 Width œ 3970 ƒ œ 496.25 or 497 Limits 70 - 566 567 - 1063 1064 - 1560 1561 - 2057 2058 - 2554 2555 - 3051 3052 - 3548 3549 - 4045 Boundaries f 30.5 - 39.5 39.5 - 48.5 48.5 - 57.5 57.5 - 66.5 12 66.5 - 75.5 13 75.5 - 84.5 84.5 - 93.5 47 16 H œ 775 L œ Width œ 775  œ 770 Range œ 770 ƒ œ 96.25 or 97 13 H œ 70 L œ 27 Range œ 70  27 œ 43 Width œ 43 ƒ œ 6.1 or Limits 27 - 33 34 - 40 41 - 47 48 - 54 55 - 61 62 - 68 69 - 75 Limits 31 - 39 40 - 48 49 - 57 58 - 66 67 - 75 76 - 84 85 - 93 Boundaries 69.5 - 566.5 566.5 - 1063.5 1063.5 - 1560.5 1560.5 - 2057.5 2057.5 - 2554.5 2554.5 - 3051.5 3051.5 - 3548.5 3548.5 - 4045.5 f 14 5 0 27 Boundaries 149.5 - 1276.5 1276.5 - 2403.5 2403.5 - 3530.5 3530.5 - 4657.5 4657.5 - 5784.5 5784.5 - 6911.5 6911.5 - 8038.5 8038.5 - 9165.5 9165.5 - 10,292.5 10,292.5 - 11,419.5 18 H œ 550 L œ 306 Range œ 550  306 œ 244 Width œ 244 ƒ œ 30.5 or 31 cf 14 19 24 24 24 25 25 27 f 2 7 3 42 cf 17 24 27 34 37 40 42 Chapter - Frequency Distributions and Graphs continued cfS 10 26 47 62 65 66 66 25 20 15 10 frequency fS 10 16 21 15 66 13 18 23 28 33 25.5 30.5 Years of Service cumulative frequency 18 continued fM , cfM = McGwire fS , cfS œ Sosa Limits Boundaries fM cfM 306 - 336 305.5 - 336.5 1 337 - 367 336.5 - 367.5 368 - 398 367.5 - 398.5 19 26 399 - 429 398.5 - 429.5 15 41 430 - 460 429.5 - 460.5 18 59 461 - 491 460.5 - 491.5 65 492 - 522 491.5 - 522.5 68 523 - 553 522.5 - 553.5 70 70 19 The percents add up to 101% They should total 100% unless rounding was used 80 60 40 20 0.5 5.5 10.5 15.5 20.5 Years of Service The majority of employees have worked for less than 11 years 50 40 30 20 10 30 25 89.598.5 98.5107.5 107.5116.5 116.5125.5 frequency frequency EXERCISE SET 2-3 125.5134.5 20 15 10 I.Q 201.5-204.5 204.5-207.5 207.5-210.5 210.5-213.5 213.5-216.5 216.5-219.5 40 30 20 25 85 94 103 112 121 130 139 frequency frequency Scores 60 I.Q 20 15 10 201 203 206 209 212 215 218 221 Scores 98.5 107.5 116.5 125.5 80 134.5 70 cumulative frequency cumulative frequency 120 100 80 60 40 20 89.5 I.Q Eighty applicants not need to enroll in the summer programs 60 50 40 30 20 10 201.5 204.5 207.5 210.5 213.5 216.5 219.5 frequency Scores 25 20 15 10 The distribution appears to be slightly left skewed 0.55.5 5.510.5 10.515.5 15.520.5 20.525.5 25.530.5 Years of Service Chapter - Frequency Distributions and Graphs 14 15 fre que ncy 12 frequency 10 10 39.85-42.85 42.85-45.85 45.85-48.85 48.85-51.85 51.85-54.85 - 6 - - - - 5 - 5 - - 6 5 5 5 5 5 4 5 54.85-57.85 Fa ta litie s M illions of Dolla rs 14 fr e qu e n cy 15 12 frequency 10 10 18 815 31 13 30 03 33 0 79 Fatalitie s 38.35 41.35 44.35 47.35 50.35 53.35 56.35 59.35 Millions of Dollars 30 20 cumulative frequency cf 35 10 30 25 69.5 20 566.5 1063.5 1560.5 2057.5 2554.5 3051.5 3548.5 4045.5 Fatalities 15 10 The data are clustered to the left There are two gaps in the histogram, one between 1560.5 and 2554.5 and the other between 3051.5 and 3548.5 The ogive shows a sharp increase in values at the beginning, followed by a leveling off of values 38.85 42.85 45.85 48.85 51.85 54.85 57.85 Millions of Dollars The distribution is left skewed or negatively skewed 25 7.512.5 12.517.5 17.522.5 22.527.5 frequency frequency 15 10 27.532.5 M PG 20 15 10 -0.527.5 55.583.5 83.5- 111.5- 139.5- 167.5111.5 139.5 167.5 195.5 Air Quality (Days ) - 1993 15 frequency 27.555.5 10 20 10 15 20 25 30 frequency 35 M PG 10 30 cumulative frequency 15 -0.527.5 20 27.5- 55.555.5 83.5 83.5- 111.5- 139.5- 167.5111.5 139.5 167.5 195.5 Air Quality (Days ) - 2002 10 7.5 12.5 17.5 22.5 27.5 32.5 M PG Chapter - Frequency Distributions and Graphs continued Both graphs are similar in that they are positively skewed Also, it looks as if the air quality has improved somewhat in that there are slightly more smaller values in 2002, which means fewer days with unacceptable levels of pollution continued frequency 15 10 35 44 53 62 71 80 89 Age 12 10 2.252.95 2.953.65 3.654.35 4.355.05 5.055.75 cumulative frequency frequency 5.756.45 Tim e 50 40 30 20 10 30.5 39.5 48.5 57.5 66.5 75.5 84.5 93.5 Age frequency 15 10 The histogram has a peak at the class of 66.5  75.5 and is somewhat negatively skewed 1.9 2.6 3.3 4.0 4.7 5.4 6.1 6.8 Tim e 20 50 frequency cumulative frequency 10 40 30 20 15 10 10 0 2.25 2.95 3.65 4.35 5.05 5.75 17.5 22.5 6.45 Tim e 22.5 27.5 27.5 32.5 32.5 37.5 37.5 42.5 42.5 47.5 % At or Above Reading Level The data values fall somewhat on the left side of the distribution The histogram is right skewed There are no gaps in the histogram frequency 20 15 10 17.5 22.5 22.5 27.5 27.5 32.5 32.5 37.5 37.5 42.5 42.5 47.5 % At or Above Math Level 10 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 30.5 - 39.5 - 48.5 - 57.5 - 66.5 - 75.5 - 84.5 39.5 48.5 57.5 66.5 75.5 84.5 93.5 Age 11 20 frequency frequency 15 15 10 4.5101.5 101.5198.5 198.5295.5 295.5392.5 392.5489.5 Acres 489.5586.5 586.5683.5 683.5780.5 Chapter - Frequency Distributions and Graphs 11 continued 13 continued relative frequency frequency 20 15 10 53 150 247 344 441 538 635 732 829 Acres 0.4 0.3 0.2 0.1 85 94 103 112 121 130 139 40 30 20 10 4.5 101.5 198.5 295.5 392.5 489.5 586.5 683.5 cumulative relative frequency cumulative frequency I Q 780.5 Acres 0.8 0.6 0.4 0.2 89.5 The proportion of applicants who need to enroll in a summer program is 0.26 or 26% 12 14 20 10 305.5 - 336.5 - 367.5 - 398.5 - 429.5 - 460.5 - 491.5 - 522.5 - 336.5 367.5 398.5 429.5 460.5 491.5 522.5 553.5 98.5 107.5 134.5 0.3 0.2 0.1 0.55.5 5.510.5 10.515.5 15.520.5 20.525.5 25.530.5 Years relative frequency fr e q u e n cy 125.5 0.4 Feet - McGwire 30 20 10 305.5 - 336.5 - 367.5 - 398.5 - 429.5 - 460.5 - 491.5 - 522.5 - 336.5 367.5 398.5 429.5 460.5 491.5 522.5 553.5 0.4 0.3 0.2 0.1 13 18 23 28 33 38 Years Feet - Sosa The histograms show that the distances of McGwire's homeruns are more variable (spread out) than Sosa's homerun distances cumulative relative frequency 13 relative frequency 116.5 I Q relative frequency fr e q u e ncy The peak is in the first class, and then the histogram is rather uniform after the first class Most of the parks have less than 101.5 thousand acres as compared with any other class of values 0.8 0.6 0.4 0.2 0.4 0.3 0.2 0.1 0.5 5.5 10.5 15.5 20.5 25.5 30.5 Years 89.598.5 98.5107.5 107.5116.5 116.5125.5 The proportion of employees who have been with the company longer than 20 years is 0.187 or 18.7% 125.5134.5 I Q 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) Chapter - Frequency Distributions and Graphs 15 continued Limits Boundaries 80 - 108 79.5 - 108.5 109 - 137 108.5 - 137.5 138 - 166 137.5 - 166.5 167 - 195 166.5 - 195.5 196 - 224 195.5 - 224.5 225 - 253 224.5 - 253.5 254 - 282 253.5 - 282.5 16 continued rf 0.17 0.28 0.04 0.20 0.22 0.04 0.04 0.99 crf 0.17 0.45 0.49 0.69 0.91 0.95 0.99* relative frequency f 13 10 2 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 11.5-19.5 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 relative frequency *due to rounding relative frequency 0.3 0.25 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0.2 0.15 7.5 15.5 23.5 31.5 0.1 39.5 47.5 55.5 63.5 Gram s 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 1.2 cumulative relative frequency Calories relative frequency 0.3 0.25 0.2 0.15 0.8 0.6 0.4 0.2 11.5 0.1 19.5 27.5 35.5 43.5 51.5 Gram s 0.05 65 94 123 152 181 210 239 268 297 The histogram is positively skewed cumulative relative frequency Calories 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 1.2 0.8 0.6 0.4 0.2 79.5 108.5 137.5 166.5 195.5 224.5 253.5 282.5 Calories The histogram has two peaks 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 rf 0.175 0.425 0.25 0.10 0.025 0.025 1.000 crf 0.175 0.600 0.850 0.950 0.975 1.000 rf 0.63 0.20 0.07 0.00 0.00 0.10 0.00 100.0 crf 0.63 0.83 0.90 0.90 0.90 1.00 1.00 59.5 Chapter - Frequency Distributions and Graphs 17 continued 18 continued fr e que n cy relative frequency 0.7 0.6 0.5 0.4 0.3 0.2 0.1 -0.527.5 27.555.5 55.583.5 50 40 30 20 10 2.25 83.5- 111.5- 139.5- 167.5111.5 139.5 167.5 195.5 2.95 3.65 4.35 5.05 5.75 6.45 Seconds relative frequency Air Quality (Days) - 2002 Based on the histograms, the older dogs have longer reaction times Also, the reaction times for older dogs is more variable 0.7 0.6 0.5 0.4 0.3 0.2 0.1 19 Limits 22 - 24 25 - 27 28 - 30 31 - 33 34 - 36 37 - 39 40 - 42 13.5 41.5 69.5 97.5 126 154 182 1.2 0.8 Xm 23 26 29 32 35 38 41 0.6 f 20 0.4 0.2 fr e q ue ncy cumulative relative frequency Air Quality (Days) - 2002 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 -0.5 27.5 55.5 83.5 112 140 168 196 Air Quality (Days) - 2002 23 18 26 29 32 35 38 41 Seconds 15 25 20 10 fr e qu e ncy fr e que ncy 20 15 10 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 21.5 24.5 27.5 30.5 33.5 36.5 39.5 42.5 Seconds fr e q u e n cy 20 15 20 a b 14 c 10 d 16 10 2.6 3.3 4.7 5.4 6.1 Seconds 10 cf 4 10 15 18 20 Chapter - Frequency Distributions and Graphs EXERCISE SET 2-4 50 Percent 40 Percent 70 30 20 60 10 50 Petroleum 40 Coal Dry Natural Hydroelectric Gas 1997 1998 30 Nuclear Other 20 10 Violent Offenses Property Offenses Weapons Other Immigration 11 10.5 10 9.5 8.5 7.5 Number of Departures Drug Offenses The majority of the money should be spent for drug rehabilitation 1999 2000 2001 2002 Year Departures increased until 2000, decreased in 2001, then increased in 2002 PA NY CT NJ Consumption (in billions) Homicides (per 100,000) 1996 ME State 11 10.5 10 9.5 8.5 1995 300 1996 1997 1998 1999 2000 2001 2002 Year 250 200 150 There is a steady increase in consumption of tobacco products 100 50 Homes Lg Companies Sm Companies Schools Govt Agencies Number of Reactors Lo cat io n The best place to market products would be to residential users 110 108 106 104 102 100 1992 1994 1996 700 1998 2000 2002 Year 600 400 300 200 120 100 100 North America Europe Asia South America Australia 80 Africa Percent Number 500 60 40 20 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 The graph shows a decline in the percentages of registered voters voting in presidential elections 11 Chapter - Frequency Distributions and Graphs 10 Personal Business Visit friends or family Work-related Leisure 12 continued 146 330 225 299 1000 14.6% 52.56° 33.0% 118.8° 22.5% 81.0° 29.9% 107.64° 100% 360° Calcium 4.7% Iron 6.2% Oxygen 45.6% Aluminum 8.4% Silicon 27.3% Per s ona l L eis u r e Other 7.8% 14 % 29 % V is it W ork 33 % 13 Career change New job Start business Retire 2.5% About "3 of the travelers visit friends or relatives, with the fewest travelling for personal business 11 Principal Residence Liquid Assets Pension Accounts Stocks, Funds, and Trusts Business & Real Estate Miscellaneous 34% 29% 21% 16% 100% 122.4° 104.4° 75.6° 57.6° 360.0° Pie chart: 7.8% 28.08° 5.0% 18.0° 6.9% 24.84° 31.6% 113.76° 46.9% 168.84° 1.8% 6.48° 100.0% 360.00° Retire 16.0% Career change 34.0% Start business 21.0% New job 29.0% Pareto chart: Mi scel l aneous 1.8% Pr i nci pal Residence 7.8% 40% Li qui d Assets 5.0% 35% 30% Pensi on Accounts 6.9% 25% 20% 15% Busi ness & Real Estate 46.9% 10% 5% 0% Stock, Funds, &Tr usts 31.6% Career change New job Start business Retire The pie graph better represents the data since we are looking at parts of a whole 12 Oxygen Silicon Aluminum Iron Calcium Other 14 a time series graph b pie graph c Pareto chart d pie graph e time series graph f Pareto chart 45.6% 164.16° 27.3% 98.28° 8.4% 30.24° 6.2% 22.32° 4.7% 16.92° 7.8% 28.08° 100.0% 360.00° 12 Chapter - Frequency Distributions and Graphs 15 4 5 6 5 9 6 4 7 7 19 4 8 8 9 20 The distribution is somewhat symmetric and unimodal The majority of the Presidents were in their 50's when inaugurated 40 16 $ % & ' ( ) * 10 30 U S 20 Japan ) " ! ' ! ! ! 1993 1994 1995 1996 1997 ! ) ! " # # * $ $ % $ * % $ $ ' & % ) % ) % * & ( * * 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 majority of automobile thefts occurred in the 50's and 80's The data is grouped towards the higher end of the distribution 21 1500 17 Variety * * ) & $ $ ) $ # $ & $ " " # $ % & ' $ & ' " ! # 1000 Variety ) 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 The distributions are similar but variety seems to be more variable than variety 22 6 0 6 6 6 N or th w U es S t A irw ay s C on ti n en ta So l ut hw Br es it is t h Ai rw Am ay er s ic an Lu Ea fth gl an e sa (G er ) 400 300 200 100 d 800 700 600 500 er ic an 1 7 Am 7 D el ta Males Number of Aircraft Females ni te 18 Veal U * ) # ! # " ! A Pareto chart is most appropriate 8 The distribution for unemployed males is more variable than the distribution for unemployed females There are more unemployed females than males world-wide 13 Chapter - Frequency Distributions and Graphs 23 Sw ed soccer balls 20% Ita Au l y st li a en Fr an Sw ce i tz er la nd D en m ar k Au st ria Be lg iu m m an y gd o er m G Ki n te d U ni te d U ni baseballs 16% footballs 20% St at es Number of Winners 90 80 70 60 50 40 30 20 10 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 tennis balls 24% More tennis balls were sold than any other type of ball Class f 11 12 13 14 15 16 17 18 19 20 21 22 20 25 The values on the C axis start at 3.5 Also there are no data values shown for the years 2004 through 2011 REVIEW EXERCISES - CHAPTER Class Newspaper Television Radio Internet golf balls 20% f 10 16 12 12 50 cf 10 14 16 18 19 19 20 How People Receive New s 3.5 Radio 24% New spaper 20% frequency Internet 24% Television 32% 2.5 1.5 0.5 B U N Count 14 22 20 18 16 14 12 10 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 B.U.N Count f 5 25 frequency Class baseball golf ball tennis ball soccer ball football 10.5-11.5 Chapter - Frequency Distributions and Graphs continued continued The distribution is negatively skewed with most of the data in the two classes 147.5  168.5 and 168.5  189.5 cumulative frequency 20 15 10 22.5 20.5 18.5 16.5 14.5 12.5 10.5 Limits 170 - 188 189 - 207 208 - 226 227 - 245 246 - 264 265 - 283 284 - 302 303 - 321 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 Boundaries 84.5 - 105.5 105.5 - 126.5 126.5 - 147.5 147.5 - 168.5 168.5 - 189.5 189.5 - 210.5 f cf 11 20 30 39 40 10 40 f 11 0 30 cf 11 20 24 29 29 29 29 30 10 fr e que ncy Limits 85 - 105 106 - 126 127 - 147 148 - 168 169 - 189 190 - 210 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 15 10 169.5- 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 Millions of Dollars 12 frequency 10 15 fr e qu e n cy 84.5105.5 105.5126.5 126.5147.5 147.5168.5 168.5189.5 189.5210.5 10 Cos t pe r M otoris t 179 198 217 236 255 274 293 312 Millions of Dollars 12 40 fr e q u e ncy frequency 10 95 116 137 158 179 30 20 10 200 169.5 188.5 207.5 226.5 245.5 264.5 283.5 302.5 321.5 Cost per M otorist frequency Millions of Dollars 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 45 40 35 30 25 20 15 10 84.5 105.5 126.5 147.5 168.5 189.5 210.5 Cost per Motorist 15 Chapter - Frequency Distributions and Graphs 11 13 Number of homicides relative frequency 0.3 0.25 0.2 0.15 0.1 0.05 900 800 700 600 500 400 300 200 100 Chicago 84.5 105.5 105.5 126.5 126.5 147.5 147.5 168.5 168.5 189.5 Washington, D C Baltimore Atlanta City Cost Per Vehicle 14 0.25 relative frequency New Orleans 189.5 210.5 500 400 300 200 100 0.2 0.15 0.1 0.05 95 116 137 158 179 200 Cost Per Vehicle 15 0.6 0.4 0.2 Wage cumulative relative frequency 0.8 84.5 105.5 126.5 147.5 168.5 189.5 210.5 Cost Per Vehicle 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 Year The minimum wage has increased over the years with the largest increase occurring between 1975 and 1980 0.4 0.3 0.2 0.1 16 169.5 - 188.5 - 207.5 - 226.5 - 245.5 - 264.5 - 283.5 - 302.5 - 188.5 207.5 226.5 245.5 264.5 283.5 302.5 321.5 250 200 150 2002 2001 2000 1999 1998 1997 1996 1995 1994 0.2 1993 1989 50 0.3 1992 100 0.4 1991 Failures r e lative fr e q ue n cy Millions of Dollars 1990 re la tive fre que ncy 12 Year 0.1 Failures decreased to only one failure in 1997, increased slightly from 1998 to 1999, decreasing through 2001, then increasing in 2002 79 98 21 234 255 274 93 31 cum ulative r e lative fr e q ue ncy Millions of Dollars 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 16 Chapter - Frequency Distributions and Graphs 21 1 2 3 17 Viewers 80 70 First Debate Second Debate 60 50 40 30 20 10 1992 1996 2000 5 7 8 8 9 2004 The peak of the distribution is in the range of 25  29 Year About the same number of people watched the first and second debates in 1992 and 1996 After that more people watched the first debate than watched the second debate 22 20 21 22 23 24 25 26 18 Other Something 8% Diff erent 12% 3 7 8 8 The distribution of aptitude scores is fairly uniform Selfsupporting 62% Extra Money 18% 0 1 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 The majority of women worked to support themselves or their families 19 Undec ided 8% No 26% Y es 66% The majority of people surveyed would like to spend the rest of their careers with their present employer 20 1 2 3 5 8 17 Chapter - Frequency Distributions and Graphs 19 House 24% Condominium 32% Apartment 20% Mobile Home 24% f 30 cf 13 15 21 23 26 30 f 13 2 25 cf 13 15 15 20 20 22 22 23 25 14 12 10 26.5 90.5 90.5 - 154.5 - 218.5 - 282.5 - 346.5 - 410.5 - 474.5 - 538.5 154.5 218.5 282.5 346.5 410.5 474.5 538.5 602.5 Num be r of M urde rs The distribution is positively skewed with one more than half of the data values in the lowest class 21 14 12 10 frequency Number 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 23 frequency 20 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 22 Limits 27 - 90 91 - 154 155 - 218 219 - 282 283 - 346 347 - 410 411 - 474 475 - 538 539 - 602 58.5 122.5 186.5 250.5 314.5 378.5 442.5 506.5 570.5 Num be r of M urde rs cumulative frequency Ite m s Purchase d Number 30 25 20 15 10 26.5 90.5 10 154.5 218.5 282.5 346.5 410.5 474.5 538.5 602.5 Num ber of Murders 24 30 25 20 15 10 400 300 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 To n s Number Item s Purchased 9.5 Item s Purchased 200 100 Paper Iron/Steel Aluminum Yard waste 18 Glass Plastics Chapter - Frequency Distributions and Graphs Fatalities 25 560 540 520 500 480 460 440 420 1998 1999 2000 2001 Year Fatalities decreased in 1999 and then increased the next two years 26 1 6 3 8 8 9 19 ... 40 42 Chapter - Frequency Distributions and Graphs continued cfS 10 26 47 62 65 66 66 25 20 15 10 frequency fS 10 16 21 15 66 13 18 23 28 33 25.5 30.5 Years of Service cumulative frequency 18 continued... 116.5125.5 frequency frequency EXERCISE SET 2-3 125.5134.5 20 15 10 I.Q 201.5-204.5 204.5-207.5 207.5-210.5 210.5-213.5 213.5-216.5 216.5-219.5 40 30 20 25 85 94 103 112 121 130 139 frequency frequency... 22.527.5 frequency frequency 15 10 27.532.5 M PG 20 15 10 -0.527.5 55.583.5 83.5- 111.5- 139.5- 167.5111.5 139.5 167.5 195.5 Air Quality (Days ) - 1993 15 frequency 27.555.5 10 20 10 15 20 25 30 frequency