{"id":179348,"date":"2024-12-30T13:58:42","date_gmt":"2024-12-30T13:58:42","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=179348"},"modified":"2024-12-30T13:58:44","modified_gmt":"2024-12-30T13:58:44","slug":"what-does-it-mean-if-a-statistic-is-resistant","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/12\/30\/what-does-it-mean-if-a-statistic-is-resistant\/","title":{"rendered":"What does it mean if a statistic is resistant"},"content":{"rendered":"\n

What does it mean if a statistic is resistant?
Choose the correct answer below.<\/p>\n\n\n\n

a.       Changing particular data values affects its value substantially.<\/p>\n\n\n\n

b.      Extreme values (very large or small) relative to the data affect its value substantially.<\/p>\n\n\n\n

c.       An estimate of its value is extremely close to its actual value.<\/p>\n\n\n\n

d.      Extreme values (very large or small) relative to the data do not affect its value substantially.<\/p>\n\n\n\n

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

The correct answer is:<\/p>\n\n\n\n

d. Extreme values (very large or small) relative to the data do not affect its value substantially.<\/strong><\/p>\n\n\n\n

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

In statistics, a resistant statistic<\/strong> is one that is not significantly influenced by outliers or extreme values in the data set. This means that when there are unusually large or small values (outliers), they do not have a substantial effect on the statistic’s value.<\/p>\n\n\n\n

For example, the median<\/strong> is a resistant statistic. The median represents the middle value of a data set when the values are arranged in order. Even if there are extreme values (outliers) in the data, they do not change the median as much as they would affect other statistics like the mean<\/strong>.<\/p>\n\n\n\n

Why is the median resistant?<\/h4>\n\n\n\n

Consider the following set of numbers:<\/p>\n\n\n\n

    \n
  • 2, 4, 6, 8, 100<\/li>\n<\/ul>\n\n\n\n

    The median<\/strong> is 6 because it is the middle value of the ordered data set. However, if the outlier (100) is removed, the median remains 6, showing that the median is not sensitive to the extreme value.<\/p>\n\n\n\n

    On the other hand, the mean<\/strong> of this data set is:<\/p>\n\n\n\n

      \n
    • (2 + 4 + 6 + 8 + 100) \/ 5 = 120 \/ 5 = 24<\/li>\n<\/ul>\n\n\n\n

      Removing the outlier would give a mean of:<\/p>\n\n\n\n

        \n
      • (2 + 4 + 6 + 8) \/ 4 = 20 \/ 4 = 5<\/li>\n<\/ul>\n\n\n\n

        Here, the mean<\/strong> is highly sensitive to the outlier (100), which is why it is not<\/strong> a resistant statistic.<\/p>\n\n\n\n

        Other examples:<\/h3>\n\n\n\n
          \n
        • The mode<\/strong>, which is the most frequent value in a data set, can also be resistant, depending on the distribution of the data.<\/li>\n\n\n\n
        • The range<\/strong>, however, is not<\/strong> resistant because it is highly affected by extreme values (it\u2019s calculated as the difference between the largest and smallest values).<\/li>\n<\/ul>\n\n\n\n

          In summary, resistant statistics, like the median, are helpful in situations where the data contains extreme values, as they provide a more accurate representation of the central tendency without being skewed by outliers.<\/p>\n","protected":false},"excerpt":{"rendered":"

          What does it mean if a statistic is resistant?Choose the correct answer below. a.       Changing particular data values affects its value substantially. b.      Extreme values (very large or small) relative to the data affect its value substantially. c.       An estimate of its value is extremely close to its actual value. d.      Extreme values (very large […]<\/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-179348","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179348","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=179348"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179348\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=179348"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=179348"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=179348"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}