Supplementary Problems<\/p>\n\n\n\n
(a) Arrange the numbers 12, 56, 42, 21, 5, 18, 10, 3, 61, 34, 65, and 24 in an array and (b) determine the range.<\/p>\n\n\n\n
Table 2.14 shows the frequency distribution for the number of minutes per week spent watching TV by 400 junior high students. With reference to this table determine:<\/p>\n\n\n\n
(a) The upper limit of the fifth class<\/p>\n\n\n\n
(b) The lower limit of the eighth class<\/p>\n\n\n\n
(c) The class mark of the seventh class<\/p>\n\n\n\n
(d) The class boundaries of the last class<\/p>\n\n\n\n
(e) The class-interval size<\/p>\n\n\n\n
(f) The frequency of the fourth class<\/p>\n\n\n\n
(g) The relative frequency of the sixth class<\/p>\n\n\n\n
(h) The percentage of students whose weekly viewing time does not exceed 600 minutes<\/p>\n\n\n\n
(i) The percentage of students with viewing times greater than or equal to 900 minutes<\/p>\n\n\n\n
(j) The percentage of students whose viewing times are at least 500 minutes but less than 1000 minutes<\/p>\n\n\n\n
Viewing Time<\/p>\n\n\n\n
Number of<\/p>\n\n\n\n
(minutes)<\/p>\n\n\n\n
Students<\/p>\n\n\n\n
300\u2013399<\/p>\n\n\n\n
14<\/p>\n\n\n\n
400\u2013499<\/p>\n\n\n\n
46<\/p>\n\n\n\n
500\u2013599<\/p>\n\n\n\n
58<\/p>\n\n\n\n
600\u2013699<\/p>\n\n\n\n
76<\/p>\n\n\n\n
700\u2013799<\/p>\n\n\n\n
68<\/p>\n\n\n\n
800\u2013899<\/p>\n\n\n\n
62<\/p>\n\n\n\n
900\u2013999<\/p>\n\n\n\n
48<\/p>\n\n\n\n
1000\u20131099<\/p>\n\n\n\n
22<\/p>\n\n\n\n
1100\u20131199<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n (a) Arrange the numbers 12, 56, 42, 21, 5, 18, 10, 3, 61, 34, 65, and 24 in an array:<\/strong><\/p>\n\n\n\n To arrange the numbers in ascending order:<\/p>\n\n\n\n Array (ascending order):<\/strong> (b) Determine the range:<\/strong><\/p>\n\n\n\n The range<\/strong> is the difference between the largest and smallest numbers in the dataset.<\/p>\n\n\n\n Range = Largest value \u2212 Smallest value Here is the frequency distribution table based on the information provided:<\/p>\n\n\n\n (a) Upper limit of the fifth class (600\u2013699 minutes):<\/strong><\/p>\n\n\n\n The upper limit of the fifth class is 699<\/strong>.<\/p>\n\n\n\n (b) Lower limit of the eighth class (1000\u20131099 minutes):<\/strong><\/p>\n\n\n\n The lower limit of the eighth class is 1000<\/strong>.<\/p>\n\n\n\n (c) Class mark of the seventh class (900\u2013999 minutes):<\/strong><\/p>\n\n\n\n The class mark is the midpoint of the class interval. For the seventh class (900\u2013999):<\/p>\n\n\n\n Class mark = (\\frac{900 + 999}{2} = \\frac{1899}{2} = 949.5)<\/p>\n\n\n\n (d) Class boundaries of the last class (1100\u20131199 minutes):<\/strong><\/p>\n\n\n\n To find the class boundaries, subtract 0.5 from the lower limit and add 0.5 to the upper limit.<\/p>\n\n\n\n Class boundaries: (e) Class-interval size:<\/strong><\/p>\n\n\n\n The class interval size is the difference between the lower limit of any class and the lower limit of the next class.<\/p>\n\n\n\n Class interval size = 400 \u2212 300 = 100 minutes<\/strong><\/p>\n\n\n\n (f) Frequency of the fourth class (600\u2013699 minutes):<\/strong><\/p>\n\n\n\n The frequency of the fourth class is 76<\/strong> students.<\/p>\n\n\n\n (g) Relative frequency of the sixth class (800\u2013899 minutes):<\/strong><\/p>\n\n\n\n Relative frequency is calculated as the frequency of the class divided by the total number of students. The total number of students is 400.<\/p>\n\n\n\n Relative frequency of the sixth class = (\\frac{62}{400} = 0.155)<\/p>\n\n\n\n (h) Percentage of students whose weekly viewing time does not exceed 600 minutes:<\/strong><\/p>\n\n\n\n To find this, we sum the frequencies for all classes that have a viewing time of 600 minutes or less (i.e., classes 300\u2013399, 400\u2013499, 500\u2013599).<\/p>\n\n\n\n Total students with \u2264 600 minutes = (14 + 46 + 58 = 118)<\/p>\n\n\n\n Percentage = (\\frac{118}{400} \\times 100 = 29.5\\%)<\/p>\n\n\n\n (i) Percentage of students with viewing times greater than or equal to 900 minutes:<\/strong><\/p>\n\n\n\n To find this, we sum the frequencies of the classes 900\u2013999, 1000\u20131099, and 1100\u20131199.<\/p>\n\n\n\n Total students with \u2265 900 minutes = (48 + 22 + 0 = 70) (assuming 1100\u20131199 has a frequency of 0 for this question)<\/p>\n\n\n\n Percentage = (\\frac{70}{400} \\times 100 = 17.5\\%)<\/p>\n\n\n\n (j) Percentage of students whose viewing times are at least 500 minutes but less than 1000 minutes:<\/strong><\/p>\n\n\n\n To find this, we sum the frequencies for the classes 500\u2013599, 600\u2013699, 700\u2013799, and 800\u2013899.<\/p>\n\n\n\n Total students with \u2265 500 and < 1000 minutes = (58 + 76 + 68 + 62 = 264)<\/p>\n\n\n\n Percentage = (\\frac{264}{400} \\times 100 = 66\\%)<\/p>\n\n\n\n In this analysis, we have found the following values for the given frequency distribution:<\/p>\n\n\n\n This provides a thorough analysis of the distribution of students’ viewing times and highlights key statistical properties like frequencies and relative percentages.<\/p>\n","protected":false},"excerpt":{"rendered":" Supplementary Problems (a) Arrange the numbers 12, 56, 42, 21, 5, 18, 10, 3, 61, 34, 65, and 24 in an array and (b) determine the range. Table 2.14 shows the frequency distribution for the number of minutes per week spent watching TV by 400 junior high students. With reference to this table determine: (a) […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-188245","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188245","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=188245"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188245\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=188245"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=188245"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=188245"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Part 1: Array and Range of Numbers<\/h3>\n\n\n\n
[ 3, 5, 10, 12, 18, 21, 24, 34, 42, 56, 61, 65 ]<\/p>\n\n\n\n
Range = 65 \u2212 3 = 62<\/strong><\/p>\n\n\n\n
\n\n\n\nPart 2: Frequency Distribution Analysis<\/h3>\n\n\n\n
Viewing Time (minutes)<\/th> Number of Students<\/th><\/tr><\/thead> 300\u2013399<\/td> 14<\/td><\/tr> 400\u2013499<\/td> 46<\/td><\/tr> 500\u2013599<\/td> 58<\/td><\/tr> 600\u2013699<\/td> 76<\/td><\/tr> 700\u2013799<\/td> 68<\/td><\/tr> 800\u2013899<\/td> 62<\/td><\/tr> 900\u2013999<\/td> 48<\/td><\/tr> 1000\u20131099<\/td> 22<\/td><\/tr> 1100\u20131199<\/td> Unknown<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Lower boundary = 1100 \u2212 0.5 = 1099.5<\/strong>
Upper boundary = 1199 + 0.5 = 1199.5<\/strong><\/p>\n\n\n\n
\n\n\n\nSummary<\/h3>\n\n\n\n
\n