As part of the President’s Challenge, students can attempt to earn the Presidential Physical Fitness Award or the National Physical Fitness Award by meeting qualifying standards in five events: curl-ups, shuttle run, sit and reach, one-mile run, and pull-ups. The qualifying standards are based on the 1985 School Population Fitness Survey. For the Presidential Award, the standard for each event is the 85th percentile of the results for a specific age group and gender among students who participated in the 1985 survey. For the National Award, the standard is the 50th percentile. To win either award, a student must meet the qualifying standard for all five events. Jane, who is 9 years old, did 40 curl-ups in one minute. Matt, who is 12 years old, also did 40 curl-ups in one minute. The qualifying standard for the Presidential Award is 39 curl-ups for Jane and 50 curl-ups for Matt. For the National Award, the standards are 30 and 40, respectively.
(a) Compare Jane’s and Matt’s performances using percentiles. Explain in language simple enough for someone who knows little statistics to understand.<\/p>\n\n\n\n
(b) Who has the higher standardized score (z-score), Jane or Matt? Justify your answer.<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n (a)<\/strong> Jane performed better relative to her age group<\/strong> than Matt because she exceeded the Presidential standard<\/strong> of 39 by 1 curl-up, while Matt did not meet<\/strong> the Presidential standard of 50 and only met the National standard<\/strong>. Therefore, Jane is likely above the 85th percentile<\/strong>, while Matt is around the 50th percentile<\/strong>.<\/p>\n\n\n\n (b)<\/strong> Jane has the higher standardized score (z-score)<\/strong> because her performance is further above the average (mean) for her age group than Matt’s. Matt is exactly at the 50th percentile (z = 0), while Jane is likely just above the 85th percentile (z \u2248 +1.04). So, Jane has a higher z-score<\/strong>.<\/p>\n\n\n\n (a) Understanding Percentiles:<\/strong><\/p>\n\n\n\n In simple terms, a percentile<\/strong> tells us how well someone did compared to others. If you are in the 85th percentile<\/strong>, it means you did better than 85 out of 100 people<\/strong> in your group. The President’s Challenge uses data from 1985 to set percentiles for each age group.<\/p>\n\n\n\n Jane is 9 years old and did 40 curl-ups<\/strong>. The Presidential Award<\/strong> standard for her age and gender is 39 curl-ups<\/strong>, which represents the 85th percentile<\/strong>. Since Jane did 1 more<\/strong> than the 85th percentile mark, she did better than more than 85%<\/strong> of students her age. This means Jane is likely at or just above the 85th percentile<\/strong>.<\/p>\n\n\n\n Matt is 12 years old and also did 40 curl-ups<\/strong>. However, for his age, the Presidential standard is 50<\/strong>, and the National standard is 40<\/strong>, which is the 50th percentile<\/strong>. This means Matt\u2019s performance was right at average<\/strong> for his age group\u2014he did better than 50% of his peers, but not better than the top 15% required for the Presidential Award.<\/p>\n\n\n\n So even though they both did 40 curl-ups, Jane\u2019s performance is much better<\/strong> compared to other 9-year-olds than Matt\u2019s is among 12-year-olds.<\/p>\n\n\n\n (b) Understanding Z-Scores:<\/strong><\/p>\n\n\n\n A z-score<\/strong> tells us how far above or below the average a performance is, in terms of standard deviations. A z-score of 0<\/strong> means average (50th percentile), positive values<\/strong> mean above average, and negative values<\/strong> mean below average.<\/p>\n\n\n\n Matt did exactly the average<\/strong> for his group (50th percentile), so his z-score is 0<\/strong>.<\/p>\n\n\n\n Jane performed just above the 85th percentile<\/strong>, which corresponds to a z-score of around +1.04<\/strong>. This tells us that Jane\u2019s score is more than one standard deviation above<\/strong> the average for her group.<\/p>\n\n\n\n Therefore, Jane has the higher z-score<\/strong>, meaning she performed better relative to her group<\/strong> than Matt did in his.<\/p>\n","protected":false},"excerpt":{"rendered":" As part of the President’s Challenge, students can attempt to earn the Presidential Physical Fitness Award or the National Physical Fitness Award by meeting qualifying standards in five events: curl-ups, shuttle run, sit and reach, one-mile run, and pull-ups. The qualifying standards are based on the 1985 School Population Fitness Survey. For the Presidential Award, […]<\/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-211459","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211459","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=211459"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211459\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=211459"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=211459"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=211459"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Correct Answer:<\/strong><\/h3>\n\n\n\n
\n\n\n\nDetailed Explanation (300+ words):<\/strong><\/h3>\n\n\n\n
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