A researcher has collected the following sample data. 15 12 16 18 15 16 17 15 12 14 The 75th percentile is <\/p>\n\n\n\n
A 16 <\/p>\n\n\n\n
B 13 <\/p>\n\n\n\n
C 14 <\/p>\n\n\n\n
D 15<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To find the 75th percentile (Q3)<\/strong> of the given data set:<\/p>\n\n\n\n The given data set is:<\/p>\n\n\n\n 12, 12, 14, 15, 15, 15, 16, 16, 17, 18<\/strong><\/p>\n\n\n\n The 75th percentile<\/strong> (Q3) is found using the formula:<\/p>\n\n\n\n [ where n<\/strong> is the number of data points.<\/p>\n\n\n\n [ This means the 75th percentile is located at the 8.25th position<\/strong>.<\/p>\n\n\n\n Using interpolation:<\/p>\n\n\n\n [ [ The closest answer among the given options is 16<\/strong>.<\/p>\n\n\n\n A) 16<\/strong><\/p>\n\n\n\n The 75th percentile (Q3)<\/strong> is the value that separates the highest 25% of the data. To find it, we use the formula P = 0.75 \u00d7 (n + 1)<\/strong>, determine its position, and interpolate if necessary. Here, the 8.25th position corresponds to 16.25<\/strong>, which rounds to 16<\/strong>, making option A the correct answer<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" A researcher has collected the following sample data. 15 12 16 18 15 16 17 15 12 14 The 75th percentile is A 16 B 13 C 14 D 15 The Correct Answer and Explanation is : To find the 75th percentile (Q3) of the given data set: Step 1: Arrange the Data in Ascending […]<\/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-187750","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187750","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=187750"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187750\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=187750"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=187750"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=187750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Arrange the Data in Ascending Order<\/h3>\n\n\n\n
Step 2: Determine the Position of the 75th Percentile<\/h3>\n\n\n\n
P = \\frac{75}{100} \\times (n + 1)
]<\/p>\n\n\n\n
P = \\frac{75}{100} \\times (10 + 1) = 0.75 \\times 11 = 8.25
]<\/p>\n\n\n\nStep 3: Find the 8.25th Position<\/h3>\n\n\n\n
\n
Q3 = 16 + 0.25 \\times (17 – 16)
]<\/p>\n\n\n\n
Q3 = 16 + 0.25 \\times 1 = 16 + 0.25 = 16.25
]<\/p>\n\n\n\nStep 4: Choose the Closest Answer<\/h3>\n\n\n\n
Correct Answer:<\/h3>\n\n\n\n
Explanation:<\/h3>\n\n\n\n