{"id":209062,"date":"2025-04-28T10:25:11","date_gmt":"2025-04-28T10:25:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=209062"},"modified":"2025-04-28T10:25:13","modified_gmt":"2025-04-28T10:25:13","slug":"in-a-sample-of-20-men-the-mean-height-was-178-cm","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/28\/in-a-sample-of-20-men-the-mean-height-was-178-cm\/","title":{"rendered":"In a sample of 20 men, the mean height was 178 cm"},"content":{"rendered":"\n

In a sample of 20 men, the mean height was 178 cm. In a sample of 30 women, the mean height was 164 cm. What was the mean height for both groups put together?<\/p>\n\n\n\n

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

To calculate the mean height for both groups put together, we need to use the weighted average<\/strong> formula. This is because the two groups (men and women) have different sample sizes, and the mean height of the combined group should account for the number of individuals in each group.<\/p>\n\n\n\n

Step-by-Step Calculation:<\/h3>\n\n\n\n
    \n
  1. Determine the total number of people<\/strong>:
    • The sample of men is 20.<\/li>
    • The sample of women is 30.<\/li><\/ul>Total number of people = 20 (men) + 30 (women) = 50<\/strong>.<\/li>\n\n\n\n
    • Calculate the total height for each group<\/strong>:\n
        \n
      • The mean height of the men is 178 cm, and there are 20 men. So, the total height for the men is: Total\u00a0height\u00a0of\u00a0men=mean\u00a0height\u00a0of\u00a0men\u00d7number\u00a0of\u00a0men=178\u2009cm\u00d720=3560\u2009cm\\text{Total height of men} = \\text{mean height of men} \\times \\text{number of men} = 178 \\, \\text{cm} \\times 20 = 3560 \\, \\text{cm}<\/li>\n\n\n\n
      • The mean height of the women is 164 cm, and there are 30 women. So, the total height for the women is: Total\u00a0height\u00a0of\u00a0women=mean\u00a0height\u00a0of\u00a0women\u00d7number\u00a0of\u00a0women=164\u2009cm\u00d730=4920\u2009cm\\text{Total height of women} = \\text{mean height of women} \\times \\text{number of women} = 164 \\, \\text{cm} \\times 30 = 4920 \\, \\text{cm}<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • Calculate the combined total height<\/strong>: The combined total height is the sum of the total height for the men and the total height for the women: Combined\u00a0total\u00a0height=3560\u2009cm+4920\u2009cm=8480\u2009cm\\text{Combined total height} = 3560 \\, \\text{cm} + 4920 \\, \\text{cm} = 8480 \\, \\text{cm}<\/li>\n\n\n\n
      • Calculate the combined mean height<\/strong>: The mean height of the combined group is the total height of both groups divided by the total number of people: Mean\u00a0height\u00a0of\u00a0both\u00a0groups=Combined\u00a0total\u00a0heightTotal\u00a0number\u00a0of\u00a0people=8480\u2009cm50=169.6\u2009cm\\text{Mean height of both groups} = \\frac{\\text{Combined total height}}{\\text{Total number of people}} = \\frac{8480 \\, \\text{cm}}{50} = 169.6 \\, \\text{cm}<\/li>\n<\/ol>\n\n\n\n

        Final Answer:<\/h3>\n\n\n\n

        The mean height for both groups put together is 169.6 cm<\/strong>.<\/p>\n\n\n\n

        Explanation:<\/h3>\n\n\n\n

        In this problem, we’re working with two separate groups of individuals, and each group has a different sample size. To combine the groups and calculate the overall mean, we must take into account the number of individuals in each group, as their contributions to the total height are weighted by their sample sizes. Simply averaging the two means would ignore the different group sizes and result in an incorrect value. The weighted average gives us a more accurate representation of the mean height for the entire population, considering that the women\u2019s group has more individuals than the men\u2019s group.<\/p>\n","protected":false},"excerpt":{"rendered":"

        In a sample of 20 men, the mean height was 178 cm. In a sample of 30 women, the mean height was 164 cm. What was the mean height for both groups put together? The correct answer and explanation is : To calculate the mean height for both groups put together, we need to use […]<\/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-209062","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/209062","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=209062"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/209062\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=209062"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=209062"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=209062"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}