{"id":279200,"date":"2025-08-03T11:45:01","date_gmt":"2025-08-03T11:45:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=279200"},"modified":"2025-08-03T11:45:04","modified_gmt":"2025-08-03T11:45:04","slug":"the-scores-on-ms-martins-statistics-quiz-had-a-mean-of-12-and-a-standard-deviation-of-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/03\/the-scores-on-ms-martins-statistics-quiz-had-a-mean-of-12-and-a-standard-deviation-of-3\/","title":{"rendered":"The scores on Ms. Martin’s statistics quiz had a mean of 12 and a standard deviation of 3."},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

Of course. The image text is incomplete and cuts off after “standard deviation of”. For this solution, we will assume the original standard deviation was 3.<\/p>\n\n\n\n

Correct Answer:<\/strong>
Ms. Martin should first multiply each quiz score by 4 and then add 27 to the result. The transformation is: New Score = 4 * (Old Score) + 27<\/strong>.<\/p>\n\n\n\n

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

This problem requires a linear transformation to adjust the statistical properties of a dataset. A linear transformation takes the form Y = aX + b, where X is the original score, Y is the new score, ‘a’ is a multiplicative factor, and ‘b’ is an additive factor.<\/p>\n\n\n\n

The key to solving this is understanding how these two factors affect the mean and standard deviation.<\/p>\n\n\n\n

    \n
  1. Effect on Standard Deviation:<\/strong>\u00a0The standard deviation, which measures the spread of the data, is only affected by multiplication or division. Adding or subtracting a constant shifts the entire dataset but does not change its spread. Therefore, the new standard deviation is calculated as: New SD = |a| * Old SD.<\/li>\n\n\n\n
  2. Effect on Mean:<\/strong>\u00a0The mean, which measures the center of the data, is affected by both multiplication and addition. The new mean is calculated as: New Mean = a * (Old Mean) + b.<\/li>\n<\/ol>\n\n\n\n

    We can solve for the transformation in two steps.<\/p>\n\n\n\n

    Step 1: Find the multiplicative factor ‘a’ to fix the standard deviation.<\/strong>
    We need to transform the original standard deviation (assumed to be 3) into the new standard deviation of 12.
    Using the formula:
    12 = a * 3
    a = 12 \/ 3
    a = 4
    This tells us that every original score must be multiplied by 4.<\/p>\n\n\n\n

    Step 2: Find the additive factor ‘b’ to fix the mean.<\/strong>
    First, we apply the multiplication from Step 1 to the original mean:
    4 * (Original Mean) = 4 * 12 = 48.
    After multiplying, our scores have a mean of 48 and a standard deviation of 12. The standard deviation is now correct, but the mean is not. We need a mean of 75. To get from 48 to 75, we must add a constant.
    b = New Mean \u2013 Intermediate Mean
    b = 75 \u2013 48
    b = 27
    This tells us we must add 27 after multiplying.<\/p>\n\n\n\n

    Combining these steps gives the complete transformation: multiply each score by 4, then add 27.<\/p>\n\n\n\n

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

    The Correct Answer and Explanation is: Of course. The image text is incomplete and cuts off after “standard deviation of”. For this solution, we will assume the original standard deviation was 3. Correct Answer:Ms. Martin should first multiply each quiz score by 4 and then add 27 to the result. The transformation is: New Score = […]<\/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-279200","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/279200","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=279200"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/279200\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=279200"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=279200"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=279200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}