{"id":9953,"date":"2022-02-05T03:15:37","date_gmt":"2022-02-04T21:45:37","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9953"},"modified":"2022-02-05T03:15:40","modified_gmt":"2022-02-04T21:45:40","slug":"mean-deviation-about-mean-and-median-formula-and-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/mean-deviation-about-mean-and-median-formula-and-examples\/","title":{"rendered":"Mean Deviation About Mean and Median – Formula and Examples"},"content":{"rendered":"

Here you will learn what is the mean deviation formula with examples.<\/p>\n

Let’s begin – <\/p>\n

Mean Deviation Formula<\/h2>\n

(i) For Ungrouped distribution :<\/strong><\/p>\n

Definition<\/strong> : If \\(x_1\\), \\(x_2\\), ….. , \\(x_n\\) are n values of a variable X, then the mean deviation from an average A (median or arithmetic mean<\/strong>) is given by<\/p>\n

\n

Mean Deviation (M.D)  = \\({\\sum_{i=1}^{n}{|x_i – A|}}\\over n\\)<\/p>\n

M.D = \\({\\sum{d_i}}\\over n\\),  where \\(d_i\\) = \\(x_i\\) – A<\/p>\n<\/blockquote>\n\n\n

Example : <\/span>Calculate the mean deviation about median from the following data : 340, 150, 210, 240, 300, 310, 320<\/p>\n

Solution : <\/span>Arranging the observations in ascending order of magnitude, we have 150, 210, 240, 300, 310, 320, 340.

\nClearly, the middle observation is 300. So, median is 300.\n <\/p>\n \n \n \n \n \n \n \n \n \n \n
\\(x_i\\)<\/td>\n \\(|d_i|\\) = \\(|x_i – 300|\\)<\/td>\n <\/tr>\n
340<\/td>\n 40<\/td>\n <\/tr>\n
150<\/td>\n 150<\/td>\n <\/tr>\n
210<\/td>\n 90<\/td>\n <\/tr>\n
240<\/td>\n 60<\/td>\n <\/tr>\n
300<\/td>\n 0<\/td>\n <\/tr>\n
310<\/td>\n 10<\/td>\n <\/tr>\n
320<\/td>\n 20<\/td>\n <\/tr>\n
Total<\/td>\n \\(d_i\\) = 370<\/td>\n <\/tr>\n <\/tbody><\/table>

<\/p>\n

\\(\\therefore\\) Mean Deviation (M.D.) = \\({\\sum{d_i}}\\over n\\) = \\(370\\over 7\\) = 52.8\n <\/p>\n\n\n

Also Read<\/strong> : What is the Formula for Mean Median and Mode<\/a><\/p>\n

(ii) For discrete frequency distribution :<\/strong><\/p>\n

Definition<\/strong> : If \\(x_i\\)\/\\(f_i\\); i = 1, 2, …. , n is the frequency distribution, then the mean deviation from an average A (median or arithmetic mean<\/strong>) is given by<\/p>\n

\n

Mean Deviation (M.D)  = \\({\\sum_{i=1}^{n}{f_i|x_i – A|}}\\over N\\)<\/p>\n

where \\({\\sum_{i=1}^{n}{f_i}}\\) = N<\/p>\n<\/blockquote>\n\n\n

Example : <\/span>Calculate the mean deviation about mean from the following data :\n <\/p>\n \n \n
\\(x_i\\)<\/td>\n 3<\/td>\n 9<\/td>\n 17<\/td>\n 23<\/td>\n 27<\/td>\n <\/tr>\n
\\(f_i\\)<\/td>\n 8<\/td>\n 10<\/td>\n 12<\/td>\n 9<\/td>\n 5<\/td>\n <\/tr>\n <\/tbody><\/table>

<\/p>\n

Solution : <\/span>Calculation of mean deviation about mean.\n <\/p>\n \n \n \n \n \n \n \n
\\(x_i\\)<\/td>\n \\(f_i\\)<\/td>\n \\(f_i x_i\\)<\/td>\n \\(|x_i – 15|\\)<\/td>\n \\(f_i|x_i – 15|\\)<\/td>\n <\/tr>\n
3<\/td>\n 8<\/td>\n 24<\/td>\n 12<\/td>\n 96<\/td>\n <\/tr>\n
9<\/td>\n 10<\/td>\n 90<\/td>\n 6<\/td>\n 60<\/td>\n <\/tr>\n
17<\/td>\n 12<\/td>\n 204<\/td>\n 2<\/td>\n 24<\/td>\n <\/tr>\n
23<\/td>\n 9<\/td>\n 207<\/td>\n 8<\/td>\n 72<\/td>\n <\/tr>\n
27<\/td>\n 5<\/td>\n 135<\/td>\n 12<\/td>\n 60<\/td>\n <\/tr>\n
<\/td>\n N = \\(\\sum{f_i}\\) = 44<\/td>\n \\(\\sum{f_ix_i}\\) = 660<\/td>\n <\/td>\n \\(\\sum{f_i|x_i – 15|}\\) = 312<\/td>\n <\/tr>\n <\/tbody><\/table>

<\/p>\n

Mean = \\(\\sum{f_ix_i}\\over N\\) = \\(660\\over 44\\) = 15

\n Mean Deviation = M.D. = \\({\\sum_{i=1}^{n}{f_i|x_i – 15|}}\\over N\\) = \\(312\\over 44\\) = 7.09

\n <\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the mean deviation formula with examples. Let’s begin –  Mean Deviation Formula (i) For Ungrouped distribution : Definition : If \\(x_1\\), \\(x_2\\), ….. , \\(x_n\\) are n values of a variable X, then the mean deviation from an average A (median or arithmetic mean) is given by Mean Deviation …<\/p>\n

Mean Deviation About Mean and Median – Formula and Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[22],"tags":[859,861,860],"yoast_head":"\nMean Deviation About Mean and Median - Formula and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the mean deviation formula about median or mean with definition and examples based on it.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/mean-deviation-about-mean-and-median-formula-and-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mean Deviation About Mean and Median - 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