{"id":205746,"date":"2025-03-25T15:42:02","date_gmt":"2025-03-25T15:42:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=205746"},"modified":"2025-03-25T15:42:04","modified_gmt":"2025-03-25T15:42:04","slug":"find-the-percentile-for-the-observed-value-in-the-following-situations","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/25\/find-the-percentile-for-the-observed-value-in-the-following-situations\/","title":{"rendered":"Find the percentile for the observed value in the following situations"},"content":{"rendered":"\n

Find the percentile for the observed value in the following situations:<\/p>\n\n\n\n

a. Quantitative reasoning GRE score of 146 (mean 5 151.3, s. d. 5 8.7).<\/p>\n\n\n\n

b. Stanford-Binet IQ score of 97 (mean 5 100, s. d. 5 15).<\/p>\n\n\n\n

c. Woman\u2019s height of 68 inches (mean 5 65 inches, s. d. 5 2.5 inches).<\/p>\n\n\n\n

d. Man\u2019s height of 68 inches (mean = 70 inches, s. d. = 3 inches).<\/p>\n\n\n\n

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

To determine the percentile rank of an observed value within a normally distributed dataset, we can follow these steps:<\/p>\n\n\n\n

    \n
  1. Calculate the Z-score<\/strong>: This standardizes the observed value relative to the dataset’s mean and standard deviation.<\/li>\n\n\n\n
  2. Convert the Z-score to a percentile<\/strong>: This indicates the percentage of data points below the observed value.<\/li>\n<\/ol>\n\n\n\n

    The Z-score is calculated using the formula:<\/p>\n\n\n\n

    [ Z = \\frac{X – \\mu}{\\sigma} ]<\/p>\n\n\n\n

    Where:<\/p>\n\n\n\n

      \n
    • ( X ) = observed value<\/li>\n\n\n\n
    • ( \\mu ) = mean of the dataset<\/li>\n\n\n\n
    • ( \\sigma ) = standard deviation of the dataset<\/li>\n<\/ul>\n\n\n\n

      Let’s apply this to each scenario:<\/p>\n\n\n\n

      a. Quantitative reasoning GRE score of 146 (mean = 151.3, s.d. = 8.7):<\/strong><\/p>\n\n\n\n

      [ Z = \\frac{146 – 151.3}{8.7} \\approx -0.61 ]<\/p>\n\n\n\n

      A Z-score of -0.61 corresponds to approximately the 27th percentile, meaning the score is higher than about 27% of test-takers.<\/p>\n\n\n\n

      b. Stanford-Binet IQ score of 97 (mean = 100, s.d. = 15):<\/strong><\/p>\n\n\n\n

      [ Z = \\frac{97 – 100}{15} \\approx -0.20 ]<\/p>\n\n\n\n

      A Z-score of -0.20 corresponds to approximately the 42nd percentile, indicating the score is higher than about 42% of individuals.<\/p>\n\n\n\n

      c. Woman\u2019s height of 68 inches (mean = 65 inches, s.d. = 2.5 inches):<\/strong><\/p>\n\n\n\n

      [ Z = \\frac{68 – 65}{2.5} \\approx 1.20 ]<\/p>\n\n\n\n

      A Z-score of 1.20 corresponds to approximately the 88th percentile, suggesting the height is greater than about 88% of women.<\/p>\n\n\n\n

      d. Man\u2019s height of 68 inches (mean = 70 inches, s.d. = 3 inches):<\/strong><\/p>\n\n\n\n

      [ Z = \\frac{68 – 70}{3} \\approx -0.67 ]<\/p>\n\n\n\n

      A Z-score of -0.67 corresponds to approximately the 25th percentile, indicating the height is taller than about 25% of men.<\/p>\n\n\n\n

      Explanation:<\/strong><\/p>\n\n\n\n

      Z-scores are a statistical measurement that describe a value’s relation to the mean of a group of values, expressed in terms of standard deviations. A Z-score of 0 indicates the value is exactly at the mean, positive Z-scores indicate values above the mean, and negative Z-scores indicate values below the mean.<\/p>\n\n\n\n

      By converting Z-scores to percentiles, we can understand the relative standing of an individual data point within a distribution. Percentiles represent the percentage of scores in a distribution that a particular score is higher than. For instance, a score at the 88th percentile is higher than 88% of the scores in the distribution.<\/p>\n\n\n\n

      To find the percentile corresponding to a Z-score, one can use a Z-score to percentile table or an online calculator. These tools provide the cumulative percentage of values below a given Z-score in a standard normal distribution.<\/p>\n\n\n\n

      Understanding these concepts is particularly useful in standardized testing, psychological assessments, and anthropometric measurements, as it allows for the comparison of individual scores to a broader population.<\/p>\n\n\n\n

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

      Find the percentile for the observed value in the following situations: a. Quantitative reasoning GRE score of 146 (mean 5 151.3, s. d. 5 8.7). b. Stanford-Binet IQ score of 97 (mean 5 100, s. d. 5 15). c. Woman\u2019s height of 68 inches (mean 5 65 inches, s. d. 5 2.5 inches). d. Man\u2019s […]<\/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-205746","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205746","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=205746"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205746\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=205746"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=205746"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=205746"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}