{"id":182455,"date":"2025-01-13T20:04:45","date_gmt":"2025-01-13T20:04:45","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=182455"},"modified":"2025-01-13T20:04:49","modified_gmt":"2025-01-13T20:04:49","slug":"caprete-tax-taxes-on-a-pack-of-cigarettes-in-dollars-lative-frequer-4ative-frequency-relative-frequency-oution-is-one-frequency-distribution-provide-a-better-summary-of-the-data-than-the-other-expl","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/13\/caprete-tax-taxes-on-a-pack-of-cigarettes-in-dollars-lative-frequer-4ative-frequency-relative-frequency-oution-is-one-frequency-distribution-provide-a-better-summary-of-the-data-than-the-other-expl\/","title":{"rendered":"caprete tax Taxes on a pack of cigarettes (in dollars) lative frequer 4ative Frequency Relative Frequency oution is one frequency distribution provide a better summary of the data than the other? Explain. leither distribution seems to show the shape of the data well. A different class size should be used"},"content":{"rendered":"\n

caprete tax Taxes on a pack of cigarettes (in dollars) lative frequer 4ative Frequency Relative Frequency oution is one frequency distribution provide a better summary of the data than the other? Explain. leither distribution seems to show the shape of the data well. A different class size should be used. The accompanying table shows the tax, in dollars, on a pack of cigarettes in 30 randamly selected cities. Complete parts (a) through (g) below. Click the icon to view the table of data. (a) Construct a frequency distribution. Use a first class having a lower class limit of 0 and a class width of 0.50. (Type inteoers or decimals. Do not round.) (b) Construct a relative frequency distribution. Use a first class having a lower class limit of 0 and a class widh of 0.50 iDnient th then davimal nlarse as neadiad I (c) Construct a frequency histogram. Choose the correct graph below. A. C. (d) Construct a relative frequency histogram. Choose the correct graph below. D. A. C. B. D. (f) Repeat parts (a)-(0) using a class width of 1 . Construct a frequoncy distribution. Construct a relative frequency distribution. (Round to two decimal places as needed.) Construct a frequency histogram. Choose the correct frequency histogram beion.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s walk through each step for the problem involving the tax on a pack of cigarettes across 30 randomly selected cities.<\/p>\n\n\n\n

Part (a) Frequency Distribution with Class Width of 0.50<\/h3>\n\n\n\n

We are asked to create a frequency distribution, using a class width of 0.50 and a lower class limit of 0. The steps to complete this are:<\/p>\n\n\n\n

    \n
  1. Determine Class Ranges<\/strong>: Start with 0 and add 0.50 to each subsequent class:\n
      \n
    • Class 1: 0.00 – 0.50<\/li>\n\n\n\n
    • Class 2: 0.50 – 1.00<\/li>\n\n\n\n
    • Class 3: 1.00 – 1.50<\/li>\n\n\n\n
    • Continue for as many classes as necessary to cover all data points.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Count the Data in Each Class<\/strong>: Look at each city’s tax data and count how many values fall into each class.<\/li>\n\n\n\n
    • Frequency Distribution Table<\/strong>: Once you have the counts, fill out the frequency table with the class ranges and their corresponding frequencies.<\/li>\n<\/ol>\n\n\n\n

      Part (b) Relative Frequency Distribution<\/h3>\n\n\n\n

      The relative frequency is calculated by dividing the frequency of each class by the total number of observations (in this case, 30).<\/p>\n\n\n\n

        \n
      1. Formula for Relative Frequency<\/strong>: Relative\u00a0Frequency=Frequency\u00a0of\u00a0ClassTotal\u00a0Number\u00a0of\u00a0Observations\\text{Relative Frequency} = \\frac{\\text{Frequency of Class}}{\\text{Total Number of Observations}} Multiply by 100 if you need percentages.<\/li>\n\n\n\n
      2. Relative Frequency Distribution Table<\/strong>: Create a new table with class ranges and their respective relative frequencies.<\/li>\n<\/ol>\n\n\n\n

        Part (c) Frequency Histogram<\/h3>\n\n\n\n

        A frequency histogram is a bar graph where:<\/p>\n\n\n\n

          \n
        • The x-axis represents the class intervals.<\/li>\n\n\n\n
        • The y-axis represents the frequencies (or counts).<\/li>\n<\/ul>\n\n\n\n

          Make sure to:<\/p>\n\n\n\n

            \n
          • Label the axes with class intervals and frequency values.<\/li>\n\n\n\n
          • Draw bars where the height of each bar corresponds to the frequency for that class.<\/li>\n<\/ul>\n\n\n\n

            Part (d) Relative Frequency Histogram<\/h3>\n\n\n\n

            Similar to the frequency histogram, but:<\/p>\n\n\n\n

              \n
            • The y-axis represents relative frequency (or percentages) instead of raw frequencies.<\/li>\n\n\n\n
            • Bars will reflect relative frequency.<\/li>\n<\/ul>\n\n\n\n

              Part (f) New Distribution with Class Width of 1<\/h3>\n\n\n\n

              Repeat the process, but now using a class width of 1 (instead of 0.50). The classes will be:<\/p>\n\n\n\n

                \n
              • Class 1: 0.00 – 1.00<\/li>\n\n\n\n
              • Class 2: 1.00 – 2.00<\/li>\n\n\n\n
              • And so on.<\/li>\n<\/ul>\n\n\n\n

                Why This Approach Works<\/h3>\n\n\n\n

                The frequency distribution and relative frequency distribution offer a concise summary of the data. A frequency distribution helps us identify how many data points fall into specific ranges, while a relative frequency distribution standardizes the data, allowing for easier comparison across different datasets. The histogram provides a visual representation of the data, allowing for a quick understanding of the distribution shape (e.g., skewed, symmetrical). The relative frequency histogram helps contextualize the data by showing the proportion of each class.<\/p>\n\n\n\n

                Each distribution type provides different insights into the data, and using the correct class width ensures a clear, interpretable summary.<\/p>\n","protected":false},"excerpt":{"rendered":"

                caprete tax Taxes on a pack of cigarettes (in dollars) lative frequer 4ative Frequency Relative Frequency oution is one frequency distribution provide a better summary of the data than the other? Explain. leither distribution seems to show the shape of the data well. A different class size should be used. The accompanying table shows the […]<\/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-182455","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/182455","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=182455"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/182455\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=182455"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=182455"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=182455"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}