A researcher has collected the following sample data: 3, 5, 12, 3, 2. the mean of the sample is 5. Compute for the value of standard deviation.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The standard deviation of the given sample data ([3, 5, 12, 3, 2]) is approximately 4.06<\/strong>.<\/p>\n\n\n\n Standard deviation measures how much the data values deviate from the mean. A higher standard deviation indicates greater variability in the dataset.<\/p>\n\n\n\n The mean (average) is calculated as:<\/p>\n\n\n\n [ Given the data: (3, 5, 12, 3, 2),<\/p>\n\n\n\n [ We subtract the mean from each data point:<\/p>\n\n\n\n [ [ Since this is a sample, we use sample variance formula<\/strong>, dividing by (n-1) instead of (n):<\/p>\n\n\n\n [ [ The standard deviation ((s)) is the square root of the variance:<\/p>\n\n\n\n [ Thus, the standard deviation of the sample is 4.06<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" A researcher has collected the following sample data: 3, 5, 12, 3, 2. the mean of the sample is 5. Compute for the value of standard deviation. The Correct Answer and Explanation is : The standard deviation of the given sample data ([3, 5, 12, 3, 2]) is approximately 4.06. Explanation: Standard deviation measures how […]<\/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-187748","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187748","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=187748"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187748\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=187748"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=187748"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=187748"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
Step 1: Compute the Mean<\/strong><\/h4>\n\n\n\n
\\text{Mean} = \\frac{\\sum X_i}{n}
]<\/p>\n\n\n\n
\\text{Mean} = \\frac{3 + 5 + 12 + 3 + 2}{5} = \\frac{25}{5} = 5
]<\/p>\n\n\n\nStep 2: Compute Each Value\u2019s Deviation from the Mean<\/strong><\/h4>\n\n\n\n
(3 – 5) = -2, \\quad (5 – 5) = 0, \\quad (12 – 5) = 7, \\quad (3 – 5) = -2, \\quad (2 – 5) = -3
]<\/p>\n\n\n\nStep 3: Square Each Deviation<\/strong><\/h4>\n\n\n\n
(-2)^2 = 4, \\quad (0)^2 = 0, \\quad (7)^2 = 49, \\quad (-2)^2 = 4, \\quad (-3)^2 = 9
]<\/p>\n\n\n\nStep 4: Compute the Variance<\/strong><\/h4>\n\n\n\n
s^2 = \\frac{\\sum (X_i – \\bar{X})^2}{n – 1}
]<\/p>\n\n\n\n
s^2 = \\frac{4 + 0 + 49 + 4 + 9}{5 – 1} = \\frac{66}{4} = 16.5
]<\/p>\n\n\n\nStep 5: Compute the Standard Deviation<\/strong><\/h4>\n\n\n\n
s = \\sqrt{16.5} \\approx 4.06
]<\/p>\n\n\n\n