{"id":188116,"date":"2025-02-06T10:48:58","date_gmt":"2025-02-06T10:48:58","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=188116"},"modified":"2025-02-06T10:49:00","modified_gmt":"2025-02-06T10:49:00","slug":"find-the-standard-deviation-for-the-following-frequency-tables-using-the-formula","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/06\/find-the-standard-deviation-for-the-following-frequency-tables-using-the-formula\/","title":{"rendered":"Find the standard deviation for the following frequency tables using the formula"},"content":{"rendered":"\n

Find the standard deviation for the following frequency tables using the formula. Check the calculations with the TI 83\/ 84.<\/p>\n\n\n\n

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

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

To calculate the standard deviation from a frequency distribution, follow these steps:<\/p>\n\n\n\n

    \n
  1. Determine the Midpoints<\/strong>: or each class interval, calculate the midpoint by averaging the lower and upper boundaries.<\/li>\n\n\n\n
  2. Compute the Mean<\/strong>: ultiply each midpoint by its corresponding frequency to find the weighted sum. Then, divide this sum by the total number of observations to obtain the mean.<\/li>\n\n\n\n
  3. Calculate Squared Deviations<\/strong>: ubtract the mean from each midpoint to find the deviation, square each deviation, and then multiply by the corresponding frequency.<\/li>\n\n\n\n
  4. Find the Variance<\/strong>: um all the squared deviations and divide by the total number of observations.<\/li>\n\n\n\n
  5. Compute the Standard Deviation<\/strong>: ake the square root of the variance.
    Example Calculation<\/strong>:<\/li>\n<\/ol>\n\n\n\n

    Consider the following frequency distribution:<\/p>\n\n\n\n

    Class Interval<\/th>Frequency (f)<\/th><\/tr><\/thead>
    10\u201319<\/td>5<\/td><\/tr>
    20\u201329<\/td>8<\/td><\/tr>
    30\u201339<\/td>12<\/td><\/tr>
    40\u201349<\/td>10<\/td><\/tr>
    50\u201359<\/td>5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
      \n
    1. Midpoints (M)<\/strong>: Class Interval Midpoint (M) 10\u201319 14.5 20\u201329 24.5 30\u201339 34.5 40\u201349 44.5 50\u201359 54.5<\/li>\n\n\n\n
    2. Mean (\u03bc)<\/strong>:<\/li>\n<\/ol>\n\n\n\n

      [ \\mu = \\frac{(14.5 \\times 5) + (24.5 \\times 8) + (34.5 \\times 12) + (44.5 \\times 10) + (54.5 \\times 5)}{5 + 8 + 12 + 10 + 5} ]
      [ \\mu = \\frac{(72.5) + (196) + (414) + (445) + (272.5)}{40} ]
      [ \\mu = \\frac{1400}{40} = 35 ]<\/p>\n\n\n\n

        \n
      1. Squared Deviations (f \u00d7 (M – \u03bc)\u00b2)<\/strong>: Class Interval Midpoint (M) Deviation (M – \u03bc) Squared Deviation (M – \u03bc)\u00b2 f \u00d7 (M – \u03bc)\u00b2 10\u201319 14.5 -20.5 420.25 2101.25 20\u201329 24.5 -10.5 110.25 882.00 30\u201339 34.5 -0.5 0.25 3.00 40\u201349 44.5 9.5 90.25 902.50 50\u201359 54.5 19.5 380.25 1901.25<\/li>\n\n\n\n
      2. Variance (\u03c3\u00b2)<\/strong>:<\/li>\n<\/ol>\n\n\n\n

        [ \\sigma^2 = \\frac{2101.25 + 882.00 + 3.00 + 902.50 + 1901.25}{40} ]
        [ \\sigma^2 = \\frac{5789.00}{40} = 144.725 ]<\/p>\n\n\n\n

          \n
        1. Standard Deviation (\u03c3)<\/strong>:<\/li>\n<\/ol>\n\n\n\n

          [ \\sigma = \\sqrt{144.725} \\approx 12.02 ]
          Using the TI-83\/84 Calculator<\/strong>:<\/p>\n\n\n\n

          . Enter Data<\/strong>: – ress [STAT]<\/code>, then select 1:Edit<\/code>. – nter midpoints into L1<\/code> and frequencies into L2<\/code>.
          . Calculate Statistics<\/strong>: – ress [STAT]<\/code>, then select CALC<\/code>, and choose 1:1-Var Stats<\/code>. – nput L1, L2<\/code> and press [ENTER]<\/code>.
          . Interpret Results<\/strong>: – he calculator will display the mean (x\u0304<\/code>) and standard deviation (\u03c3x<\/code> for population, Sx<\/code> for sample).
          or a detailed walkthrough, refer to this video:
          \ue200video\ue202Calculating Standard Deviation on the TI-83 Plus and TI-84 Plus\ue202turn0search3\ue201<\/p>\n","protected":false},"excerpt":{"rendered":"

          Find the standard deviation for the following frequency tables using the formula. Check the calculations with the TI 83\/ 84. The Correct Answer and Explanation is : To calculate the standard deviation from a frequency distribution, follow these steps: Consider the following frequency distribution: Class Interval Frequency (f) 10\u201319 5 20\u201329 8 30\u201339 12 40\u201349 […]<\/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-188116","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188116","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=188116"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188116\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=188116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=188116"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=188116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}