What is the mean absolute deviation of the following set of data?
10,4,12,4,2,10,10,6<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To calculate the Mean Absolute Deviation (MAD) of the given data set (10, 4, 12, 4, 2, 10, 10, 6), follow these steps:<\/p>\n\n\n\n First, find the mean of the data set.<\/p>\n\n\n\n [ Next, compute the absolute deviation of each data point from the mean:<\/p>\n\n\n\n Now, find the mean of these absolute deviations:<\/p>\n\n\n\n [ Now, divide by the number of values:<\/p>\n\n\n\n [ The Mean Absolute Deviation (MAD) of the data set (10, 4, 12, 4, 2, 10, 10, 6) is approximately 3.31<\/strong>.<\/p>\n\n\n\n Mean Absolute Deviation is a statistical measure that quantifies the dispersion or spread of a set of data points around the mean. Unlike variance, which squares the deviations, MAD focuses on the absolute values of these deviations, making it more intuitive in some contexts. MAD is particularly useful in fields such as finance, meteorology, and quality control, where understanding the variability of data is crucial.<\/p>\n\n\n\n By calculating MAD, analysts can assess how much individual data points deviate from the average, helping to identify trends, anomalies, or consistency within the data. A lower MAD indicates that the data points are closely clustered around the mean, while a higher MAD signifies greater variability. Thus, MAD serves as a valuable tool for data analysis and decision-making processes.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the mean absolute deviation of the following set of data?10,4,12,4,2,10,10,6 The Correct Answer and Explanation is : To calculate the Mean Absolute Deviation (MAD) of the given data set (10, 4, 12, 4, 2, 10, 10, 6), follow these steps: Step 1: Calculate the Mean First, find the mean of the data set. […]<\/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-144130","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144130","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=144130"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144130\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=144130"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=144130"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=144130"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Calculate the Mean<\/h3>\n\n\n\n
\\text{Mean} = \\frac{\\text{Sum of all values}}{\\text{Number of values}} = \\frac{10 + 4 + 12 + 4 + 2 + 10 + 10 + 6}{8} = \\frac{58}{8} = 7.25
]<\/p>\n\n\n\nStep 2: Calculate the Absolute Deviations<\/h3>\n\n\n\n
\n
Step 3: Calculate the Mean of the Absolute Deviations<\/h3>\n\n\n\n
\\text{Sum of absolute deviations} = 2.75 + 3.25 + 4.75 + 3.25 + 5.25 + 2.75 + 2.75 + 1.25 = 26.5
]<\/p>\n\n\n\n
\\text{MAD} = \\frac{26.5}{8} = 3.3125
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n
Explanation of Mean Absolute Deviation<\/h3>\n\n\n\n