{"id":10217,"date":"2022-02-26T15:01:57","date_gmt":"2022-02-26T09:31:57","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10217"},"modified":"2022-02-27T20:20:16","modified_gmt":"2022-02-27T14:50:16","slug":"weighted-mean-formula-and-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/weighted-mean-formula-and-examples\/","title":{"rendered":"Weighted Mean – Formula and Examples"},"content":{"rendered":"

Here you will learn what is weighted mean formula and how to calculate weighted mean with examples.<\/p>\n

Let’s begin –<\/p>\n

Weighted Mean Formula<\/h2>\n

If \\(w_1\\), \\(w_2\\), ……\\(w_n\\) are the weights assigned to the values \\(x_1\\), \\(x_2\\), …..\\(x_n\\) respectively then their weighted mean is defined as<\/p>\n

\n

Weighted mean = \\(w_1x_1 + w_2x_2 +……+ w_nx_n\\over {w_1 +…….+ w_n}\\) = \\({\\sum_{i=1}^{n}w_ix_i}\\over {\\sum_{i=1}^{n}w_i}\\)<\/p>\n<\/blockquote>\n

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

The weights represent the relative importance of the values of the variable x. For example, prices are usually weighted by the relative quantities involved.<\/p>\n\n\n

Example : <\/span>Calculate the mean and the weighted mean for the following data of marks in a class X examination as per the weights attached to each other.\n\t\t\t <\/p>\n\t\t\t\t \n\t\t\t\t \n\t\t\t\t \n\t\t\t\t \n\t\t\t\t \n\t\t\t\t \n\t\t\t\t
Subject<\/td>\n\t\t\t\t Marks<\/td>\n\t\t\t\t Weights<\/td>\n <\/tr>\n
English<\/td>\n\t\t\t\t 62<\/td>\n\t\t\t\t 1<\/td>\n\t\t\t\t <\/tr>\n\t\t\t\t
Mathematics<\/td>\n\t\t\t\t 83<\/td>\n\t\t\t\t 3<\/td>\n\t\t\t\t <\/tr>\n
Science<\/td>\n\t\t\t\t 79<\/td>\n\t\t\t\t 3<\/td>\n\t\t\t\t <\/tr>\n
Social science<\/td>\n\t\t\t\t 74<\/td>\n\t\t\t\t 2<\/td>\n\t\t\t\t <\/tr>\n
Hindi<\/td>\n\t\t\t\t 77<\/td>\n\t\t\t\t 2<\/td>\n\t\t\t\t <\/tr>\n\t\t\t\t<\/tbody><\/table>

<\/p>\n

Solution : <\/span><\/p>\n\t\t\t\t \n\t\t\t\t \n\t\t\t\t \n\t\t\t\t \n\t\t\t\t \n\t\t\t\t \n\t\t\t\t \n
Subject<\/td>\n\t\t\t\t Marks \\((x_i)\\)<\/td>\n\t\t\t\t Weights \\((w_i)\\)<\/td>\n Weights \\((w_ix_i)\\)<\/td>\n <\/tr>\n
English<\/td>\n\t\t\t\t 62<\/td>\n\t\t\t\t 1<\/td>\n 62<\/td>\n\t\t\t\t <\/tr>\n\t\t\t\t
Mathematics<\/td>\n\t\t\t\t 83<\/td>\n\t\t\t\t 3<\/td>\n 249<\/td>\n\t\t\t\t <\/tr>\n
Science<\/td>\n\t\t\t\t 79<\/td>\n\t\t\t\t 3<\/td>\n 237<\/td>\n\t\t\t\t <\/tr>\n
Social science<\/td>\n\t\t\t\t 74<\/td>\n\t\t\t\t 2<\/td>\n 148<\/td>\n\t\t\t\t <\/tr>\n
Hindi<\/td>\n\t\t\t\t 77<\/td>\n\t\t\t\t 2<\/td>\n 154<\/td>\n <\/tr>\n
<\/td>\n\t\t\t\t \\(\\sum x_i\\) = 375<\/td>\n\t\t\t\t \\(\\sum w_i\\) = 11<\/td>\n \\(\\sum w_ix_i\\) = 850<\/td> \n\t\t\t\t <\/tr>\n\t\t\t\t<\/tbody><\/table>\nMean = \\(\\sum x_i\\over n\\) = \\(375\\over 5\\) = 75

\nWeighted Mean = \\({\\sum_{i=1}^{n}w_ix_i}\\over {\\sum_{i=1}^{n}w_i}\\) = \\(850\\over 11\\) = 77.27

\nHence, Mean = 75 and the weighted mean = 77.27

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

Here you will learn what is weighted mean formula and how to calculate weighted mean with examples. Let’s begin – Weighted Mean Formula If \\(w_1\\), \\(w_2\\), ……\\(w_n\\) are the weights assigned to the values \\(x_1\\), \\(x_2\\), …..\\(x_n\\) respectively then their weighted mean is defined as Weighted mean = \\(w_1x_1 + w_2x_2 +……+ w_nx_n\\over {w_1 +…….+ …<\/p>\n

Weighted Mean – Formula and Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","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":[895,896,893,894],"yoast_head":"\nWeighted Mean - Formula and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is weighted mean formula and how to calculate weighted mean with examples.\" \/>\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\/weighted-mean-formula-and-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Weighted Mean - 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