{"id":2883,"date":"2022-02-06T19:01:41","date_gmt":"2022-02-06T19:01:41","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=2883"},"modified":"2022-02-06T19:01:41","modified_gmt":"2022-02-06T19:01:41","slug":"how-to-find-the-mean-absolute-deviation","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/how-to-find-the-mean-absolute-deviation\/","title":{"rendered":"How to find the mean absolute deviation"},"content":{"rendered":"[vc_section full_width=&#8221;stretch_row&#8221; content_placement=&#8221;middle&#8221; css=&#8221;.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}&#8221; el_id=&#8221;bg-sec&#8221;][vc_row full_width=&#8221;stretch_row_content&#8221; el_class=&#8221;faaaq&#8221;][vc_column width=&#8221;1\/12&#8243;][\/vc_column][vc_column width=&#8221;1\/2&#8243; css=&#8221;.vc_custom_1633761494145{border-radius: 1px !important;}&#8221;][vc_row_inner content_placement=&#8221;middle&#8221; el_class=&#8221;topheadingg&#8221;][vc_column_inner width=&#8221;1\/6&#8243;][vc_single_image image=&#8221;2283&#8243; img_size=&#8221;full&#8221;][\/vc_column_inner][vc_column_inner width=&#8221;5\/6&#8243;][vc_column_text]\n<h5>How to find the mean absolute deviation<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=&#8221;headingnew&#8221;]Concept[\/vc_column_text][vc_column_text]Calculate the mean absolute deviation of a given set of data.[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Rules[\/vc_column_text][vc_column_text]Steps to finding mean absolute deviation: \u200b<br \/>\n1. Find the <a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/find-the-mean\">mean<\/a>.\u200b<br \/>\n2. Find the absolute value of the differences between each value in the data set and the mean. \u200b<br \/>\n3. Find the average of the absolute values of the differences between each value in the data set and the mean. \u200b[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Example[\/vc_column_text][vc_column_text]<strong><span style=\"color: #16a085;\">The table below shows the number of calories in different types of cookies. Find the mean absolute deviation of the set of data. Round the final answer to the nearest hundredth.<\/span><\/strong><\/p>\n<table style=\"text-align: center; margin-top: -14px; width: 240px; font-size: 17px; font-family: Lucida Sans Unicode,Lucida Grande,sans-serif;\" border=\"1\">\n<tbody>\n<tr style=\"text-align: center; border: 1;\">\n<th style=\"background-color: #af7ac5; padding: 2px; text-align: center; width: 70px;\" colspan=\"4\"><span style=\"color: #ffffff;\"><span style=\"font-size: 18px;\"><span style=\"font-family: Lucida Sans Unicode,Lucida Grande,sans-serif;\">Number of Calories in Various Cookies<\/span><\/span><\/span><\/th>\n<\/tr>\n<tr style=\"text-align: center;\">\n<td>40<\/td>\n<td>50<\/td>\n<td>43<\/td>\n<td>49<\/td>\n<\/tr>\n<tr style=\"text-align: center;\">\n<td>64<\/td>\n<td>22<\/td>\n<td>56<\/td>\n<td>47<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Solution[\/vc_column_text][vc_column_text]The first step in finding the mean absolute deviation is calculating the mean.<\/p>\n<p>Mean (Average)\u00a0 = \u00a0<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&amp;space;\\frac{Sum&amp;space;\\:&amp;space;of&amp;space;\\:the\\:&amp;space;data\\:&amp;space;values}{Number\\:&amp;space;of\\:&amp;space;data\\:&amp;space;values}\" alt=\"\\fn_phv \\frac{Sum \\: of \\:the\\: data\\: values}{Number\\: of\\: data\\: values}\" align=\"absmiddle\" \/><\/p>\n<p>Mean (Average)\u00a0 =\u00a0 <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&amp;space;\\frac{(40+50+43+49+64+22+56+47)}{8}\" alt=\"\\fn_phv \\frac{(40+50+43+49+64+22+56+47)}{8}\" align=\"absmiddle\" \/><\/p>\n<p>Mean (Average)\u00a0 =\u00a0 <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&amp;space;\\frac{371}{8}\" alt=\"\\fn_phv \\frac{371}{8}\" align=\"absmiddle\" \/>\u00a0 = 46.375<\/p>\n<p>Next we need to take the absolute value of each data value minus the mean.<br \/>\n\u250240 &#8211; 46.375\u2502 = 6.375 ,<\/p>\n<p>\u250250 &#8211; 46.375\u2502 = 3.625 ,<\/p>\n<p>\u250243 &#8211; 46.375\u2502 = 3.375 ,<\/p>\n<p>\u250249 &#8211; 46.375\u2502 = 2.625 ,<\/p>\n<p>\u250264 &#8211; 46.375\u2502 = 17.625 ,<\/p>\n<p>\u250222 &#8211; 46.375\u2502 = 24.375 ,<\/p>\n<p>\u250256 &#8211; 9.625\u2502= 9.625 ,<\/p>\n<p>\u250247 &#8211; 46.375\u2502= 0.625<\/p>\n<p>Add all of the values together.<br \/>\n6.375 + 3.625 + 3.375 + 2.625 + 17.625 + 24.375 + 9.625 + 0.625 = 68.25<\/p>\n<p>Lastly, to find the mean absolute deviation we take our total and divide it by the number of data values we started with.<\/p>\n<p>Mean absolute deviation\u00a0 =\u00a0 <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&amp;space;\\frac{68.25}{8}\" alt=\"\\fn_phv \\frac{68.25}{8}\" align=\"absmiddle\" \/>\u00a0 =\u00a0 8.53125, which we round to <span style=\"color: red;\">8.53<\/span>[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Practice How to Find the Mean Absolute Deviation[\/vc_column_text][vc_row_inner el_class=&#8221;boxxborder&#8221;][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><strong><span style=\"color: #16a085;\">Drag the correct answer choice in the blank to complete the statement.<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/measures-of-variation\"><img loading=\"lazy\" class=\"alignnone wp-image-2725 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/11-6.png\" alt=\"\" width=\"381\" height=\"125\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/11-6.png 381w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/11-6-300x98.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><\/a>[\/vc_column_text][vc_single_image image=&#8221;2159&#8243; img_size=&#8221;full&#8221; alignment=&#8221;right&#8221; onclick=&#8221;custom_link&#8221; link=&#8221;https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/measures-of-variation&#8221;][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=&#8221;boxxborder&#8221;][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><strong><span style=\"color: #16a085;\">The table below shows the number of eggs collected each day at a local household. Find the mean absolute deviation of the data set. Round the final answer to the nearest hundredth.<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/measures-of-variation\"><img loading=\"lazy\" class=\"alignnone wp-image-2727 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/12-1.png\" alt=\"\" width=\"375\" height=\"141\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/12-1.png 375w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/12-1-300x113.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><\/a>[\/vc_column_text][vc_single_image image=&#8221;2159&#8243; img_size=&#8221;full&#8221; alignment=&#8221;right&#8221; onclick=&#8221;custom_link&#8221; link=&#8221;https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/measures-of-variation&#8221;][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=&#8221;boxxborder&#8221;][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><strong><span style=\"color: #16a085;\">The two tables below show the number of students in dorms for two different universities. Find the mean absolute deviations and fill in the blanks. Round your answers to the nearest hundredths.<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/measures-of-variation\"><img loading=\"lazy\" class=\"alignnone wp-image-2729 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/13.png\" alt=\"\" width=\"353\" height=\"202\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/13.png 353w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/13-300x172.png 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/a>[\/vc_column_text][vc_single_image image=&#8221;2159&#8243; img_size=&#8221;full&#8221; alignment=&#8221;right&#8221; onclick=&#8221;custom_link&#8221; link=&#8221;https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/measures-of-variation&#8221;][\/vc_column_inner][\/vc_row_inner][vc_empty_space][\/vc_column][vc_column width=&#8221;1\/3&#8243; css=&#8221;.vc_custom_1633369011398{margin-bottom: 50px !important;}&#8221;][vc_row_inner el_class=&#8221;stickynotee&#8221;][vc_column_inner][vc_single_image image=&#8221;2265&#8243; img_size=&#8221;full&#8221; alignment=&#8221;center&#8221; css_animation=&#8221;fadeIn&#8221; css=&#8221;.vc_custom_1633509989314{border-radius: 10px !important;}&#8221; el_class=&#8221;stickypin&#8221;][vc_column_text]<strong>Mean:<\/strong> is the average of the data set.<\/p>\n<p><strong>Range:<\/strong> It is the difference between the highest and lowest values in the set.<\/p>\n<p><strong>Mean absolute deviation:<\/strong> is an indicator of the spread of the data, or how far each data value is from the mean. The higher the mean absolute deviation, the further spread the data is from the mean.<\/p>\n<p><strong>Standard deviation:<\/strong> is a calculated value that shows how the data deviates from the mean of the data.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=&#8221;boxxborder2&#8243;]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/find-the-mean\"><span style=\"color: #ed5600;\">Find the Mean<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/find-the-range\"><span style=\"color: #ed5600;\">Find Range<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/select-an-appropriate-display\"><span style=\"color: #ed5600;\">Select an Appropriate Display<\/span><\/a>[\/vc_column_text][vc_column_text el_class=&#8221;boxxborder2&#8243; css=&#8221;.vc_custom_1635233527537{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 35px !important;}&#8221;]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/making-predictions\"><span style=\"color: #333399;\">Making Predictions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/unbiased-and-biased-samples\"><span style=\"color: #333399;\">Unbiased and Biased Samples<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/misleading-graphs-and-statistics\"><span style=\"color: #333399;\">Misleading Graphs and Statistics<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/compare-populations\"><span style=\"color: #333399;\">Compare Populations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/select-an-appropriate-display\"><span style=\"color: #333399;\">Select an Appropriate Display<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/scatter-plots\"><span style=\"color: #333399;\">Scatter Plots<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/lines-of-best-fit\"><span style=\"color: #333399;\">Lines of Best Fit<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/two-way-tables\"><span style=\"color: #333399;\">Two-Way Tables<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/descriptive-statistics\"><span style=\"color: #333399;\">Descriptive Statistics<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/measures-of-variation\"><span style=\"color: #333399;\">Measures of Variation<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/analyze-data-distribution\"><span style=\"color: #333399;\">Analyze Data Distribution<\/span><\/a>[\/vc_column_text][vc_row_inner equal_height=&#8221;yes&#8221; el_class=&#8221;btninlinespacing&#8221;][vc_column_inner][vc_btn title=&#8221;Grade 1&#8243; color=&#8221;warning&#8221; link=&#8221;url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||&#8221;][vc_btn title=&#8221;Grade 2&#8243; color=&#8221;danger&#8221; link=&#8221;url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||&#8221;][vc_btn title=&#8221;Grade 3&#8243; color=&#8221;violet&#8221; link=&#8221;url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F3rd-grade%2Fmaths|title:Grade%203%20Math||&#8221;][vc_btn title=&#8221;Grade 4&#8243; color=&#8221;blue&#8221; link=&#8221;url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F4th-grade%2Fmaths|title:Grade%204%20Math||&#8221;][vc_btn title=&#8221;Grade 5&#8243; color=&#8221;green&#8221; link=&#8221;url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F5th-grade%2Fmaths|title:Grade%205%20Math||&#8221;][vc_btn title=&#8221;Grade 6&#8243; color=&#8221;info&#8221; link=&#8221;url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F6th-grade%2Fmaths|title:Grade%206%20Math||&#8221;][vc_btn title=&#8221;Grade 7&#8243; 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el_id=&#8221;bg-sec&#8221;][vc_row full_width=&#8221;stretch_row_content&#8221; el_class=&#8221;faaaq&#8221;][vc_column width=&#8221;1\/12&#8243;][\/vc_column][vc_column width=&#8221;1\/2&#8243; css=&#8221;.vc_custom_1633761494145{border-radius: 1px !important;}&#8221;][vc_row_inner content_placement=&#8221;middle&#8221; el_class=&#8221;topheadingg&#8221;][vc_column_inner width=&#8221;1\/6&#8243;][vc_single_image image=&#8221;2283&#8243; img_size=&#8221;full&#8221;][\/vc_column_inner][vc_column_inner width=&#8221;5\/6&#8243;][vc_column_text] How to find the mean absolute deviation [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=&#8221;headingnew&#8221;]Concept[\/vc_column_text][vc_column_text]Calculate the mean absolute deviation of a given set of data.[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Rules[\/vc_column_text][vc_column_text]Steps to finding mean absolute deviation: \u200b 1. Find the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How to find the mean absolute deviation | Oryx Learning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/oryxlearning.com\/learn\/how-to-find-the-mean-absolute-deviation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to find the mean absolute deviation\" \/>\n<meta property=\"og:description\" content=\"[vc_section full_width=&#8221;stretch_row&#8221; content_placement=&#8221;middle&#8221; css=&#8221;.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}&#8221; el_id=&#8221;bg-sec&#8221;][vc_row full_width=&#8221;stretch_row_content&#8221; el_class=&#8221;faaaq&#8221;][vc_column width=&#8221;1\/12&#8243;][\/vc_column][vc_column width=&#8221;1\/2&#8243; css=&#8221;.vc_custom_1633761494145{border-radius: 1px !important;}&#8221;][vc_row_inner content_placement=&#8221;middle&#8221; el_class=&#8221;topheadingg&#8221;][vc_column_inner width=&#8221;1\/6&#8243;][vc_single_image image=&#8221;2283&#8243; img_size=&#8221;full&#8221;][\/vc_column_inner][vc_column_inner width=&#8221;5\/6&#8243;][vc_column_text] How to find the mean absolute deviation [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=&#8221;headingnew&#8221;]Concept[\/vc_column_text][vc_column_text]Calculate the mean absolute deviation of a given set of data.[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Rules[\/vc_column_text][vc_column_text]Steps to finding mean absolute deviation: \u200b 1. 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