{"id":156276,"date":"2022-03-26T01:34:37","date_gmt":"2022-03-25T20:04:37","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/standard-error-of-the-mean-definition-explanation-and-solved-examples\/"},"modified":"2022-12-22T21:38:08","modified_gmt":"2022-12-22T16:08:08","slug":"standard-error-of-the-mean-definition-explanation-and-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/standard-error-of-the-mean\/","title":{"rendered":"Standard Error of The Mean \u2013 Definition, Explanation and Solved Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/standard-error-of-the-mean\/#Standard_Error_of_the_Mean_Definition\" title=\"Standard Error of the Mean Definition\">Standard Error of the Mean Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/standard-error-of-the-mean\/#Standard_Error_of_Mean\" title=\"Standard Error of Mean\">Standard Error of Mean<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/standard-error-of-the-mean\/#How_to_Calculate_Standard_Error_of_Mean\" title=\"How to Calculate Standard Error of Mean\">How to Calculate Standard Error of Mean<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/standard-error-of-the-mean\/#1_Calculate_the_Standard_Error_of_the_Mean_for_the_Given_Data_510152025\" title=\"1. Calculate the Standard Error of the Mean for the Given Data: 5,10,15,20,25.\">1. Calculate the Standard Error of the Mean for the Given Data: 5,10,15,20,25.<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Standard_Error_of_the_Mean_Definition\"><\/span>Standard Error of the Mean Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The standard error of the mean (SEM) is a measure of the variability of the sample mean. It is calculated as the standard deviation of the sample mean divided by the square root of the sample size. The SEM is a measure of the precision of the sample mean.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156275 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/standard-error-of-the-mean-definition-explanation-and-solved-examples.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/standard-error-of-the-mean-definition-explanation-and-solved-examples.jpg?v=1648238674 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/standard-error-of-the-mean-definition-explanation-and-solved-examples-300x212.jpg?v=1648238674 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<p>&nbsp;<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Standard_Error_of_Mean\"><\/span>Standard Error of Mean<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The standard error of the mean (SEM) is a statistic that measures the variability of the sample mean around the population mean. It is calculated as the standard deviation of the sample mean divided by the square root of the sample size. The SEM is a measure of the precision of the sample mean.<\/p>\n<p>The SEM is used to calculate confidence intervals for the population mean. A 95% confidence interval is calculated as the population mean \u00b1 1.96 SEM. This means that there is a 95% probability that the population mean lies within 1.96 SEM of the sample mean.<\/p>\n<p>The SEM can also be used to calculate the probability of obtaining a sample mean that is different from the population mean. This is known as the p-value. The p-value is the probability of obtaining a sample mean that is more extreme than the sample mean. The smaller the p-value, the more likely it is that the sample mean is different from the population mean.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Calculate_Standard_Error_of_Mean\"><\/span>How to Calculate Standard Error of Mean<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The standard error of the mean (SEM) is a measure of the variability of the sample mean around the population mean. It is calculated as the standard deviation of the sample mean divided by the square root of the sample size.<\/p>\n<p>The SEM is important because it is used to calculate confidence intervals around the population mean. A 95% confidence interval means that there is a 95% probability that the population mean lies within the confidence interval.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"1_Calculate_the_Standard_Error_of_the_Mean_for_the_Given_Data_510152025\"><\/span>1. Calculate the Standard Error of the Mean for the Given Data: 5,10,15,20,25.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Standard Error of the Mean is 2.5.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Standard Error of the Mean Definition The standard error of the mean (SEM) is a measure of the variability of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Standard Error of The Mean \u2013 Definition, Explanation and Solved Examples","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about standard error of the mean topic of maths in details explained by subject experts on infinitylearn.com. 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