Question 1: [20 marks] The longest-running Broadway show, with more than 12,000 performances, is Phantom of...

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Question 1: [20 marks] The longest-running Broadway show, with more than 12,000 performances, is Phantom of the Opera. A sample of Broadway shows was obtained, and the number of performances of each was recorded. Download the data file for this question. a. [5=2,2,1 marks] Find the sample mean and the sample median number of performances. Leave your answers to one decimal places. What do these values suggest about the shape of the distribution? Show your work. b. [42, 2, marks] Find the sample variance and the sample standard deviation. Leave answers to one decimal place. Show your work c. [43, 1, marks] Find the proportion of observations within 1 standard deviation of the mean, within 2 standard deviations of the mean, and within 3 standard deviations of the mean. Leave answers to two decimal places. What do these proportions suggest about the shape of the distribution? d. [3=1,1,1 marks] Find the first quartile, the third quartile, and the interquartile range. Show your work. Leave answers in one decimal place. e. [4=3,1 marks] Construct a modified box plot for the performance data. Use this graph to describe the distribution in terms of symmetry, skewness, variability, and outliers. Question 1: [20 marks] The longest-running Broadway show, with more than 12,000 performances, is Phantom of the Opera. A sample of Broadway shows was obtained, and the number of performances of each was recorded. Download the data file for this question. a. [5=2,2,1 marks] Find the sample mean and the sample median number of performances. Leave your answers to one decimal places. What do these values suggest about the shape of the distribution? Show your work. b. [42,2, marks] Find the sample variance and the sample standard deviation. Leave answers to one decimal place. Show your work c. [4=3, 1, marks] Find the proportion of observations within 1 standard deviation of the mean, within 2 standard deviations of the mean, and within 3 standard deviations of the mean. Leave answers to two decimal places. What do these proportions suggest about the shape of the distribution? d. [3=1,1,1 marks] Find the first quartile, the third quartile, and the interquartile range. Show your work. Leave answers in one decimal place. e. [4=3,1 marks] Construct a modified box plot for the performance data. Use this graph to describe the distribution in terms of symmetry, skewness, variability, and outliers. A B C D E F G H 1 Show Performaces 2 The Phantom of the Opera 3 Chicago (1996 Revival) 4 The Lion King 5 Cats 12526 8851 8453 7485 6 Les Miserables 6680 7 A Chorus Line 6137 8 Wicked 5988 9 Oh! Calcutta! (1976 Revival) 5959 10 Mamma Mia! 5773 11 Beauty and the Beast 5461 12 Rent 13 Jersey Boys 14 Miss Saigon 5123 4642 4092 15 42nd Street 3486 16 Grease 3388 17 Fiddler on the Roof 3242 18 Life with Father 3224 19 Tobacco Road 3182 20 The Book of Mormon 2906 21 Hello, Dolly! 2844 22 My Fair Lady 23 Hairspray 24 Mary Poppins 25 Avenue Q 2717 2642 2619 2534 26 The Producers 2502 27 Cabaret (1998 Revival) 2377 28 Annie 2377 29 Man of La Mancha 2328 3330 A B C D E F G H 29 Man of La Mancha 30 Rock of Ages 31 Abie's Irish Rose 32 Oklahoma! 33 Kinky Boots 34 Smokey Joe's Cafe 35 Pippin 36 South Pacific 37 The Magic Show 38 Aida 39 Gemini 40 Deathtrap 41 Harvey 2328 2328 2327 2212 2050 2036 1944 1925 1920 1852 1819 1793 1775 42 Dancin' 1774 43 La Cage aux Folles 1761 44 Hair 1750 45 Beautiful: The Carole King Musical 1728 46 The Wiz 1672 47 Aladdin 1658 48 Born Yesterday 1642 49 Crazy For You 1622 50 Ain't Misbehavin' 1604 51 Monty Python's Spamalot 1575 52 Mary, Mary 1572 53 Evita 54 The Voice of the Turtle 55 Matilda The Musical 56 Jekyll & Hyde 57 Barefoot in the Park 1567 1557 1554 1543 1532 A B C D E F G H 57 Barefoot in the Park 58 42nd Street (2001 Revival) 59 Dreamgirls 60 Mame 61 Grease (1994 Revival) 62 Same Time, Next Year 63 Arsenic and Old Lace 64 The Sound of Music 1532 1524 1521 1508 1505 1453 1444 1443 65 Me and My Girl 1420 66 How to Succeed in Business Without Really Trying 1417 67 Hellzapoppin 1404 68 The Music Man 1375 69 Funny Girl 1348 70 Mummenschanz 71 Oh! Calcutta! 1326 1316 72 Billy Elliot: The Musical 1312 73 Movin' Out 74 Brighton Beach Memoirs 1303 1299 75 Angel Street 1295 76 Lightnin' 77 Promises, Promises 78 The King and I 1291 1281 1246 79 Cactus Flower 1234 80 Sleuth 1222 81 Torch Song Trilogy 1222 82 1776 1217 83 Equus 1209 84 Sugar Babies 1208 85 Guys and Dolls Oc In the Heights 1200 1105 A B C D E F G H 85 Guys and Dolls 86 In the Heights 87 Amadeus 88 Once 89 Memphis 90 Cabaret 91 Mister Roberts 92 Annie Get Your Gun 1200 1185 1181 1168 1166 1165 1157 1147 93 Guys and Dolls (1992 Revival) 1143 94 The Seven Year Itch 1141 95 The 25th Annual Putnam County Spelling Bee 1136 96 Bring in 'da Noise, Bring in 'da Funk 1135 97 Butterflies Are Free 1128 98 Pins and Needles 99 Plaza Suite 100 Fosse 1108 1097 1093 101 They're Playing Our Song 1082 102 Kiss Me, Kate 1077 103 Hamilton 1077 104 Spider-Man Turn Off the Dark 1066 105 Don't Bother Me, I Can't Cope 1065 106 The Pajama Game 1063 107 Shenandoah 1050 108 Annie Get Your Gun (1999 Revival) 1045 109 The Teahouse of the August Moon 1027 110 Les Miserables (2014 revival) 1024 111 Damn Yankees 1019 112 Grand Hotel 113 Contact 1017 1010 4007 A B C D E F G H 95 The 25th Annual Putnam County Spelling Bee 1136 96 Bring in 'da Noise, Bring in 'da Funk 1135 97 Butterflies Are Free 98 Pins and Needles 99 Plaza Suite 100 Fosse 101 They're Playing Our Song 102 Kiss Me, Kate 103 Hamilton 104 Spider-Man Turn Off the Dark 1128 1108 1097 1093 1082 1077 1077 1066 105 Don't Bother Me, I Can't Cope 1065 106 The Pajama Game 1063 107 Shenandoah 1050 108 Annie Get Your Gun (1999 Revival) 1045 109 The Teahouse of the August Moon 1027 110 Les Miserables (2014 revival) 1024 111 Damn Yankees 112 Grand Hotel 113 Contact 114 Never Too Late 115 Beatlemania 116 Big River 1019 1017 1010 1007 1006 1005 1004 117 Newsies 118 119 120 121 122 123 101 Question 1: [20 marks] The longest-running Broadway show, with more than 12,000 performances, is Phantom of the Opera. A sample of Broadway shows was obtained, and the number of performances of each was recorded. Download the data file for this question. a. [5=2,2,1 marks] Find the sample mean and the sample median number of performances. Leave your answers to one decimal places. What do these values suggest about the shape of the distribution? Show your work. b. [42, 2, marks] Find the sample variance and the sample standard deviation. Leave answers to one decimal place. Show your work c. [43, 1, marks] Find the proportion of observations within 1 standard deviation of the mean, within 2 standard deviations of the mean, and within 3 standard deviations of the mean. Leave answers to two decimal places. What do these proportions suggest about the shape of the distribution? d. [3=1,1,1 marks] Find the first quartile, the third quartile, and the interquartile range. Show your work. Leave answers in one decimal place. e. [4=3,1 marks] Construct a modified box plot for the performance data. Use this graph to describe the distribution in terms of symmetry, skewness, variability, and outliers. Question 1: [20 marks] The longest-running Broadway show, with more than 12,000 performances, is Phantom of the Opera. A sample of Broadway shows was obtained, and the number of performances of each was recorded. Download the data file for this question. a. [5=2,2,1 marks] Find the sample mean and the sample median number of performances. Leave your answers to one decimal places. What do these values suggest about the shape of the distribution? Show your work. b. [42,2, marks] Find the sample variance and the sample standard deviation. Leave answers to one decimal place. Show your work c. [4=3, 1, marks] Find the proportion of observations within 1 standard deviation of the mean, within 2 standard deviations of the mean, and within 3 standard deviations of the mean. Leave answers to two decimal places. What do these proportions suggest about the shape of the distribution? d. [3=1,1,1 marks] Find the first quartile, the third quartile, and the interquartile range. Show your work. Leave answers in one decimal place. e. [4=3,1 marks] Construct a modified box plot for the performance data. Use this graph to describe the distribution in terms of symmetry, skewness, variability, and outliers. A B C D E F G H 1 Show Performaces 2 The Phantom of the Opera 3 Chicago (1996 Revival) 4 The Lion King 5 Cats 12526 8851 8453 7485 6 Les Miserables 6680 7 A Chorus Line 6137 8 Wicked 5988 9 Oh! Calcutta! (1976 Revival) 5959 10 Mamma Mia! 5773 11 Beauty and the Beast 5461 12 Rent 13 Jersey Boys 14 Miss Saigon 5123 4642 4092 15 42nd Street 3486 16 Grease 3388 17 Fiddler on the Roof 3242 18 Life with Father 3224 19 Tobacco Road 3182 20 The Book of Mormon 2906 21 Hello, Dolly! 2844 22 My Fair Lady 23 Hairspray 24 Mary Poppins 25 Avenue Q 2717 2642 2619 2534 26 The Producers 2502 27 Cabaret (1998 Revival) 2377 28 Annie 2377 29 Man of La Mancha 2328 3330 A B C D E F G H 29 Man of La Mancha 30 Rock of Ages 31 Abie's Irish Rose 32 Oklahoma! 33 Kinky Boots 34 Smokey Joe's Cafe 35 Pippin 36 South Pacific 37 The Magic Show 38 Aida 39 Gemini 40 Deathtrap 41 Harvey 2328 2328 2327 2212 2050 2036 1944 1925 1920 1852 1819 1793 1775 42 Dancin' 1774 43 La Cage aux Folles 1761 44 Hair 1750 45 Beautiful: The Carole King Musical 1728 46 The Wiz 1672 47 Aladdin 1658 48 Born Yesterday 1642 49 Crazy For You 1622 50 Ain't Misbehavin' 1604 51 Monty Python's Spamalot 1575 52 Mary, Mary 1572 53 Evita 54 The Voice of the Turtle 55 Matilda The Musical 56 Jekyll & Hyde 57 Barefoot in the Park 1567 1557 1554 1543 1532 A B C D E F G H 57 Barefoot in the Park 58 42nd Street (2001 Revival) 59 Dreamgirls 60 Mame 61 Grease (1994 Revival) 62 Same Time, Next Year 63 Arsenic and Old Lace 64 The Sound of Music 1532 1524 1521 1508 1505 1453 1444 1443 65 Me and My Girl 1420 66 How to Succeed in Business Without Really Trying 1417 67 Hellzapoppin 1404 68 The Music Man 1375 69 Funny Girl 1348 70 Mummenschanz 71 Oh! Calcutta! 1326 1316 72 Billy Elliot: The Musical 1312 73 Movin' Out 74 Brighton Beach Memoirs 1303 1299 75 Angel Street 1295 76 Lightnin' 77 Promises, Promises 78 The King and I 1291 1281 1246 79 Cactus Flower 1234 80 Sleuth 1222 81 Torch Song Trilogy 1222 82 1776 1217 83 Equus 1209 84 Sugar Babies 1208 85 Guys and Dolls Oc In the Heights 1200 1105 A B C D E F G H 85 Guys and Dolls 86 In the Heights 87 Amadeus 88 Once 89 Memphis 90 Cabaret 91 Mister Roberts 92 Annie Get Your Gun 1200 1185 1181 1168 1166 1165 1157 1147 93 Guys and Dolls (1992 Revival) 1143 94 The Seven Year Itch 1141 95 The 25th Annual Putnam County Spelling Bee 1136 96 Bring in 'da Noise, Bring in 'da Funk 1135 97 Butterflies Are Free 1128 98 Pins and Needles 99 Plaza Suite 100 Fosse 1108 1097 1093 101 They're Playing Our Song 1082 102 Kiss Me, Kate 1077 103 Hamilton 1077 104 Spider-Man Turn Off the Dark 1066 105 Don't Bother Me, I Can't Cope 1065 106 The Pajama Game 1063 107 Shenandoah 1050 108 Annie Get Your Gun (1999 Revival) 1045 109 The Teahouse of the August Moon 1027 110 Les Miserables (2014 revival) 1024 111 Damn Yankees 1019 112 Grand Hotel 113 Contact 1017 1010 4007 A B C D E F G H 95 The 25th Annual Putnam County Spelling Bee 1136 96 Bring in 'da Noise, Bring in 'da Funk 1135 97 Butterflies Are Free 98 Pins and Needles 99 Plaza Suite 100 Fosse 101 They're Playing Our Song 102 Kiss Me, Kate 103 Hamilton 104 Spider-Man Turn Off the Dark 1128 1108 1097 1093 1082 1077 1077 1066 105 Don't Bother Me, I Can't Cope 1065 106 The Pajama Game 1063 107 Shenandoah 1050 108 Annie Get Your Gun (1999 Revival) 1045 109 The Teahouse of the August Moon 1027 110 Les Miserables (2014 revival) 1024 111 Damn Yankees 112 Grand Hotel 113 Contact 114 Never Too Late 115 Beatlemania 116 Big River 1019 1017 1010 1007 1006 1005 1004 117 Newsies 118 119 120 121 122 123 101

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a To find the sample mean and median number of performances we first need to calculate them from the ... View the full answer