{"id":252478,"date":"2025-07-11T10:26:19","date_gmt":"2025-07-11T10:26:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=252478"},"modified":"2025-07-11T10:26:21","modified_gmt":"2025-07-11T10:26:21","slug":"consider-the-following-data","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/11\/consider-the-following-data\/","title":{"rendered":"Consider the following data"},"content":{"rendered":"\n

Consider the following data: 1,6,7,3,5,2 Step 1 of 3: Calculate the value of the sample variance. Round your answer to one decimal place. Step 2 of 3: Calculate the value of the sample standard deviation. Round your answer to one decimal place. Step 3 of 3: Calculate the value of the range<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Step 1: Calculate the Sample Variance<\/h3>\n\n\n\n

To calculate the sample variance, we follow these steps:<\/p>\n\n\n\n

    \n
  1. Find the mean<\/strong> of the data.<\/li>\n\n\n\n
  2. Subtract the mean<\/strong> from each data point and square the result.<\/li>\n\n\n\n
  3. Sum up all the squared differences<\/strong>.<\/li>\n\n\n\n
  4. Divide by (n – 1)<\/strong>, where n<\/em> is the number of data points.<\/li>\n<\/ol>\n\n\n\n

    Given data: 1, 6, 7, 3, 5, 2<\/p>\n\n\n\n

    Step 1.1: Find the mean<\/h4>\n\n\n\n

    Mean=1+6+7+3+5+26=246=4\\text{Mean} = \\frac{1 + 6 + 7 + 3 + 5 + 2}{6} = \\frac{24}{6} = 4Mean=61+6+7+3+5+2\u200b=624\u200b=4<\/p>\n\n\n\n

    Step 1.2: Calculate the squared differences from the mean<\/h4>\n\n\n\n
      \n
    • (1 – 4)\u00b2 = (-3)\u00b2 = 9<\/li>\n\n\n\n
    • (6 – 4)\u00b2 = (2)\u00b2 = 4<\/li>\n\n\n\n
    • (7 – 4)\u00b2 = (3)\u00b2 = 9<\/li>\n\n\n\n
    • (3 – 4)\u00b2 = (-1)\u00b2 = 1<\/li>\n\n\n\n
    • (5 – 4)\u00b2 = (1)\u00b2 = 1<\/li>\n\n\n\n
    • (2 – 4)\u00b2 = (-2)\u00b2 = 4<\/li>\n<\/ul>\n\n\n\n

      Step 1.3: Sum of the squared differences<\/h4>\n\n\n\n

      9+4+9+1+1+4=289 + 4 + 9 + 1 + 1 + 4 = 289+4+9+1+1+4=28<\/p>\n\n\n\n

      Step 1.4: Calculate the sample variance<\/h4>\n\n\n\n

      Sample Variance=286\u22121=285=5.6\\text{Sample Variance} = \\frac{28}{6 – 1} = \\frac{28}{5} = 5.6Sample Variance=6\u2212128\u200b=528\u200b=5.6<\/p>\n\n\n\n

      So, the sample variance is 5.6<\/strong> (rounded to one decimal place).<\/p>\n\n\n\n

      \n\n\n\n

      Step 2: Calculate the Sample Standard Deviation<\/h3>\n\n\n\n

      The sample standard deviation is the square root of the sample variance: Sample Standard Deviation=5.6\u22482.37\\text{Sample Standard Deviation} = \\sqrt{5.6} \\approx 2.37Sample Standard Deviation=5.6\u200b\u22482.37<\/p>\n\n\n\n

      Rounding to one decimal place, the sample standard deviation is 2.4<\/strong>.<\/p>\n\n\n\n

      \n\n\n\n

      Step 3: Calculate the Range<\/h3>\n\n\n\n

      The range is simply the difference between the maximum and minimum values in the dataset:<\/p>\n\n\n\n

        \n
      • Maximum value = 7<\/li>\n\n\n\n
      • Minimum value = 1<\/li>\n<\/ul>\n\n\n\n

        Range=7\u22121=6\\text{Range} = 7 – 1 = 6Range=7\u22121=6<\/p>\n\n\n\n

        So, the range is 6<\/strong>.<\/p>\n\n\n\n

        \n\n\n\n

        Summary:<\/h3>\n\n\n\n
          \n
        • Sample Variance<\/strong> = 5.6<\/li>\n\n\n\n
        • Sample Standard Deviation<\/strong> = 2.4<\/li>\n\n\n\n
        • Range<\/strong> = 6<\/li>\n<\/ul>\n\n\n\n

          These values provide insights into the spread and variability of the dataset. The sample variance quantifies how spread out the data points are from the mean, the standard deviation gives a more intuitive measure of spread in the same units as the original data, and the range offers a simple but effective way of describing the extent between the smallest and largest data points.<\/p>\n\n\n\n

          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

          Consider the following data: 1,6,7,3,5,2 Step 1 of 3: Calculate the value of the sample variance. Round your answer to one decimal place. Step 2 of 3: Calculate the value of the sample standard deviation. Round your answer to one decimal place. Step 3 of 3: Calculate the value of the range The Correct Answer […]<\/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-252478","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252478","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=252478"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252478\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=252478"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=252478"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=252478"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}