{"id":671,"date":"2020-07-27T13:33:00","date_gmt":"2020-07-27T17:33:00","guid":{"rendered":"https:\/\/openbooks.macewan.ca\/rcommander\/?post_type=part&#038;p=671"},"modified":"2025-05-07T17:54:56","modified_gmt":"2025-05-07T21:54:56","slug":"chapter-6-distribution-of-the-sample-mean-and-the-central-limit-theorem","status":"publish","type":"part","link":"https:\/\/openbooks.macewan.ca\/introstats\/part\/chapter-6-distribution-of-the-sample-mean-and-the-central-limit-theorem\/","title":{"raw":"Chapter 6: Distribution of the Sample Mean and the Central Limit Theorem","rendered":"Chapter 6: Distribution of the Sample Mean and the Central Limit Theorem"},"content":{"raw":"<h2>Overview<\/h2>\r\nThere are two types of statistics: descriptive and inferential. Chapters 1 and 2 focus on descriptive statistics; chapters 3, 4, and 5 are about probability (topics from these chapters will reappear in later chapters); chapters seven and all chapters after that will focus on inferential statistics. This chapter introduces the distribution of the sample mean and the central limit theorem, which provides a foundation for inferential statistics.\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">Learning Objectives<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nAs a result of completing this chapter, you will be able to do the following:\r\n<ul>\r\n \t<li>Explain the difference between a statistic and a parameter.<\/li>\r\n \t<li>Explain the relationships among a parameter, an estimator, and a point estimate.<\/li>\r\n \t<li>Describe how to obtain the sampling distribution of the sample mean.<\/li>\r\n \t<li>Explain and describe the distribution of sample mean in three aspects: mean, standard deviation, and shape.<\/li>\r\n \t<li>Explain the central limit theorem in plain English.<\/li>\r\n \t<li>Apply the central limit theorem to answer questions about the sample mean.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>","rendered":"<h2>Overview<\/h2>\n<p>There are two types of statistics: descriptive and inferential. Chapters 1 and 2 focus on descriptive statistics; chapters 3, 4, and 5 are about probability (topics from these chapters will reappear in later chapters); chapters seven and all chapters after that will focus on inferential statistics. This chapter introduces the distribution of the sample mean and the central limit theorem, which provides a foundation for inferential statistics.<\/p>\n<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">Learning Objectives<\/header>\n<div class=\"textbox__content\">\n<p>As a result of completing this chapter, you will be able to do the following:<\/p>\n<ul>\n<li>Explain the difference between a statistic and a parameter.<\/li>\n<li>Explain the relationships among a parameter, an estimator, and a point estimate.<\/li>\n<li>Describe how to obtain the sampling distribution of the sample mean.<\/li>\n<li>Explain and describe the distribution of sample mean in three aspects: mean, standard deviation, and shape.<\/li>\n<li>Explain the central limit theorem in plain English.<\/li>\n<li>Apply the central limit theorem to answer questions about the sample mean.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n","protected":false},"parent":0,"menu_order":6,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-671","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/671","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":7,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/671\/revisions"}],"predecessor-version":[{"id":5505,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/671\/revisions\/5505"}],"wp:attachment":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/media?parent=671"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/contributor?post=671"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/license?post=671"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}