{"id":7076,"date":"2023-10-05T00:00:00","date_gmt":"2023-10-05T04:00:00","guid":{"rendered":"https:\/\/www.sisense.com\/weighted-vs-unweighted-averages\/"},"modified":"2024-09-23T15:36:09","modified_gmt":"2024-09-23T19:36:09","slug":"weighted-vs-unweighted-averages","status":"publish","type":"post","link":"https:\/\/www.sisense.com\/blog\/weighted-vs-unweighted-averages\/","title":{"rendered":"Weighted vs. Unweighted averages"},"content":{"rendered":"<p>\r\n\r\nWhen summarizing statistics across multiple categories, analysts often have to decide between using weighted and unweighted averages.\r\n\r\n\r\n\r\n\r\n\r\nAn <strong>unweighted average<\/strong> is essentially your familiar method of taking the mean. Let&#8217;s say 0% of users logged into my site on Day 1, and 100% of users logged in on Day 2. The unweighted average for the 2 days combined would be (0% + 100%)\/2 = 50%.\r\n\r\n\r\n\r\n\r\n\r\n<strong>Weighted averages<\/strong> take the sample size into consideration. Let&#8217;s say in the example above, there was only 1 user enrolled on Day 1 and 4 users enrolled on Day 2 &#8211; making a total of 5 users over the 2 days. The weighted average is 0% * (1\/5) + 100% * (4\/5) = 80%. Typically, users want to calculate weighted averages because it prevents skewing from categories with smaller sample sizes.\r\n\r\n\r\n\r\n\r\n\r\nIf we want to add a row with a weighted average, we can accomplish this via SQL as shown in the example below (note that this example leverages Redshift syntax).\r\n\r\n\r\n\r\n\r\n\r\nLet&#8217;s walk through an example of how to calculate each of these measures! Let&#8217;s say our original table, t1, contains the following data:\r\n\r\n\r\n\r\n\r\n<figure class=\"wp-block-image size-full fancybox\"><img decoding=\"async\" class=\"wp-image-83125\" src=\"https:\/\/cdn.sisense.com\/wp-content\/uploads\/Original-Table1.png\" alt=\"Original table\"><\/figure>\r\n\r\n\r\n\r\n\r\nHere is how to calculate the weighted average. To add an extra &#8216;Total&#8217; row, I used a SQL Union all.\r\n\r\n\r\n\r\n\r\n<pre class=\"wp-block-code\"><code>select\r\n  month::varchar(12)\r\n  , (round(perc_purchases_over_10_dollars * 100, 2) || '%') as perc_purchases_over_10_dollars\r\n  , sample_size\r\nfrom\r\n  t1\r\nunion all\r\nselect\r\n  'weighted avg'\r\n  , (round(sum(perc_purchases_over_10_dollars * sample_size) \/ sum(sample_size) * 100, 2) || '%')\r\n  , sum(sample_size)\r\nfrom\r\n  t1\r\ngroup by\r\n  1<\/code><\/pre><p>\r\n\r\nThe result looks like this:\r\n\r\n\r\n\r\n\r\n<figure class=\"wp-block-image size-full fancybox\"><img decoding=\"async\" class=\"wp-image-83131\" src=\"https:\/\/cdn.sisense.com\/wp-content\/uploads\/Weighted-Averages.png\" alt=\"Weighted averages\"><\/figure>\r\n\r\n\r\n\r\n\r\nOn the contrary, if we would prefer to use an unweighted average, we can simply union an avg() of each of the categories.&nbsp; (The additional round\/decimal casting is for formatting purposes.)\r\n\r\n\r\n\r\n\r\n<\/p><pre class=\"wp-block-code\"><code>select\r\n  month::varchar(15)\r\n  , (round(perc_purchases_over_10_dollars * 100, 2) || '%') as perc_purchases_over_10_dollars\r\n  , sample_size\r\nfrom\r\n  t1\r\nunion all\r\nselect\r\n  'unweighted avg'\r\n  , (round(avg(perc_purchases_over_10_dollars) * 100, 2)::decimal(6,2) || '%')\r\n  , sum(sample_size) as sample_size\r\nfrom\r\n  t1<\/code><\/pre><p>\r\n\r\nHere, we can see that the results differ from the weighted average example (12.04% as opposed to 12.00%).\r\n\r\n\r\n\r\n\r\n<figure class=\"wp-block-image size-full fancybox\"><img decoding=\"async\" class=\"wp-image-83137\" src=\"https:\/\/cdn.sisense.com\/wp-content\/uploads\/Unweighted-Averages.png\" alt=\"Unweighted averages\"><\/figure>\r\n\r\n\r\n\r\n\r\nNote that unweighted and weighted averages are equal if each category has the same sample size.\r\n\r\n<\/p><\/p><!-- \/wp:code --><!-- wp:paragraph --><!-- \/wp:code --><!-- wp:paragraph -->\r\n","protected":false},"excerpt":{"rendered":"<p>When summarizing statistics across multiple categories, analysts often have to decide between using weighted and unweighted averages. An unweighted average is essentially your familiar method of taking the mean. Let&#8217;s say 0% of users logged into my site on Day&#8230;<\/p>\n","protected":false},"author":4,"featured_media":7265,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_searchwp_excluded":"","footnotes":"","_links_to":"","_links_to_target":""},"categories":[44],"tags":[472],"application":[10],"buyer-role":[],"buyer-stage":[],"department":[],"industry":[],"topic":[],"class_list":["post-7076","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tech-talk","tag-data-team","application-cloud-data-teams"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v23.5 (Yoast SEO v23.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Weighted vs. Unweighted Averages | Sisense<\/title>\n<meta name=\"description\" content=\"When summarizing statistics across multiple categories, analysts often have to decide between using weighted and unweighted averages.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.sisense.com\/blog\/weighted-vs-unweighted-averages\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Weighted vs. Unweighted averages\" \/>\n<meta property=\"og:description\" content=\"When summarizing statistics across multiple categories, analysts often have to decide between using weighted and unweighted averages. 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