{"id":1894,"date":"2021-09-15T12:09:52","date_gmt":"2021-09-15T12:09:52","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=1894"},"modified":"2022-02-07T18:51:39","modified_gmt":"2022-02-07T18:51:39","slug":"introduction-to-the-central-limit-theorem-for-sample-means-averages","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/introduction-to-the-central-limit-theorem-for-sample-means-averages\/","title":{"raw":"Introduction to The Central Limit Theorem for Sample Means (Averages)","rendered":"Introduction to The Central Limit Theorem for Sample Means (Averages)"},"content":{"raw":"<h2>What you\u2019ll learn to do: calculate mean, standard deviation, probabilities and percentiles for the sampling distribution<\/h2>\r\n<img class=\"size-medium wp-image-1895 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/09\/15120821\/pexels-craig-adderley-1561147-300x200.jpg\" alt=\"Coca cola cans in a cardboard container\" width=\"300\" height=\"200\" \/>To estimate the number of ounces in soda cans, we can take a sample. If the sample size is large enough, the distribution of sample means will be approximately normal. This allows us to use normal distribution calculations for probabilities of observing certain values for a sample mean. This concept is known as the central limit theorem.","rendered":"<h2>What you\u2019ll learn to do: calculate mean, standard deviation, probabilities and percentiles for the sampling distribution<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-1895 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/09\/15120821\/pexels-craig-adderley-1561147-300x200.jpg\" alt=\"Coca cola cans in a cardboard container\" width=\"300\" height=\"200\" \/>To estimate the number of ounces in soda cans, we can take a sample. If the sample size is large enough, the distribution of sample means will be approximately normal. This allows us to use normal distribution calculations for probabilities of observing certain values for a sample mean. This concept is known as the central limit theorem.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1894\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Selective Focus Photography of Red Coca-cola Can Lot on Box. <strong>Authored by<\/strong>: Craig Adderley. <strong>Provided by<\/strong>: Pexels. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.pexels.com\/photo\/selective-focus-photography-of-red-coca-cola-can-lot-on-box-1561147\/\">https:\/\/www.pexels.com\/photo\/selective-focus-photography-of-red-coca-cola-can-lot-on-box-1561147\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Selective Focus Photography of Red Coca-cola Can Lot on Box\",\"author\":\"Craig Adderley\",\"organization\":\"Pexels\",\"url\":\"https:\/\/www.pexels.com\/photo\/selective-focus-photography-of-red-coca-cola-can-lot-on-box-1561147\/\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1894","chapter","type-chapter","status-publish","hentry"],"part":262,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1894","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1894\/revisions"}],"predecessor-version":[{"id":3709,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1894\/revisions\/3709"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/262"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1894\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=1894"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=1894"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=1894"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=1894"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}