{"id":689,"date":"2021-08-13T17:13:42","date_gmt":"2021-08-13T17:13:42","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=689"},"modified":"2023-12-05T08:37:00","modified_gmt":"2023-12-05T08:37:00","slug":"summary-definitions-of-probability-statistics-and-key-terms","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-definitions-of-probability-statistics-and-key-terms\/","title":{"raw":"Summary: Definitions of Probability, Statistics, and Key Terms","rendered":"Summary: Definitions of Probability, Statistics, and Key Terms"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">When data is gathered from a sample, we can use statistics, like means and proportions, to summarize the data.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">When data is gathered from a sample that is representative of the population, inferential statistics can be used to make conclusions about the population's parameters.<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<strong>average<\/strong>\u00a0(mean): a number that describes the central tendency of the data\r\n\r\n<strong>categorical variable:<\/strong> variables that take on values that are names or labels\r\n\r\n<strong>data<\/strong>\u00a0(singular is datum): a set of observations (a set of possible outcomes). Most data can be put into two groups: qualitative (an attribute whose value is indicated by a label) or quantitative (an attribute whose value is indicated by a number).\r\n\r\n<strong>dot plot<\/strong>:\u00a0a number line and dots (or points) positioned above the number line\r\n\r\n<strong>integers<\/strong>:\u00a0includes the negative natural numbers in the set of whole numbers, e.g. [latex]\\{\\dots,-3,-2,-1,0,1,2,3,\\dots\\}[\/latex]\r\n\r\n<strong>irrational numbers<\/strong>:\u00a0the set of numbers that are not rational, are nonrepeating, and are nonterminating, e.g. [latex]\\{h|h\\text{ is not a rational number}\\}[\/latex]\r\n\r\n<strong>natural numbers<\/strong>:\u00a0the numbers used for counting, e.g. [latex]\\{1,2,3,\\dots\\}[\/latex]\r\n\r\n<strong>numerical variable:<\/strong> variables that take on values that are indicated by numbers\r\n\r\n<strong>parameter:<\/strong> a number that is used to represent a population characteristic and that generally cannot be determined easily\r\n\r\n<strong>population:\u00a0<\/strong>all individuals, objects, or measurements whose properties are being studied\r\n\r\n<strong>probability:<\/strong> a number between zero and one, inclusive, that gives the likelihood that a specific event will occur\r\n\r\n<strong>proportion:<\/strong> the number of successes divided by the total number in the sample\r\n\r\n<strong>rational numbers:<\/strong>\u00a0fractions written as [latex]\\{\\frac{m}{n}|m\\text{ and }n\\text{ are integers and }n\\ne 0\\}[\/latex]\r\n\r\n<strong>representative sample:<\/strong> a subset of the population that has the same characteristics as the population\r\n\r\n<strong>sample:<\/strong> a subset of the population studied\r\n\r\n<strong>statistic:<\/strong> a numerical characteristic of the sample; a statistic estimates the corresponding population parameter\r\n\r\n<strong>variable:<\/strong> a characteristic of interest for each person or object in a population\r\n\r\n<strong>whole numbers<\/strong>:\u00a0the set of natural numbers plus zero, e.g. [latex]\\{0,1,2,3,\\dots\\}[\/latex]","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">When data is gathered from a sample, we can use statistics, like means and proportions, to summarize the data.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">When data is gathered from a sample that is representative of the population, inferential statistics can be used to make conclusions about the population&#8217;s parameters.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>average<\/strong>\u00a0(mean): a number that describes the central tendency of the data<\/p>\n<p><strong>categorical variable:<\/strong> variables that take on values that are names or labels<\/p>\n<p><strong>data<\/strong>\u00a0(singular is datum): a set of observations (a set of possible outcomes). Most data can be put into two groups: qualitative (an attribute whose value is indicated by a label) or quantitative (an attribute whose value is indicated by a number).<\/p>\n<p><strong>dot plot<\/strong>:\u00a0a number line and dots (or points) positioned above the number line<\/p>\n<p><strong>integers<\/strong>:\u00a0includes the negative natural numbers in the set of whole numbers, e.g. [latex]\\{\\dots,-3,-2,-1,0,1,2,3,\\dots\\}[\/latex]<\/p>\n<p><strong>irrational numbers<\/strong>:\u00a0the set of numbers that are not rational, are nonrepeating, and are nonterminating, e.g. [latex]\\{h|h\\text{ is not a rational number}\\}[\/latex]<\/p>\n<p><strong>natural numbers<\/strong>:\u00a0the numbers used for counting, e.g. [latex]\\{1,2,3,\\dots\\}[\/latex]<\/p>\n<p><strong>numerical variable:<\/strong> variables that take on values that are indicated by numbers<\/p>\n<p><strong>parameter:<\/strong> a number that is used to represent a population characteristic and that generally cannot be determined easily<\/p>\n<p><strong>population:\u00a0<\/strong>all individuals, objects, or measurements whose properties are being studied<\/p>\n<p><strong>probability:<\/strong> a number between zero and one, inclusive, that gives the likelihood that a specific event will occur<\/p>\n<p><strong>proportion:<\/strong> the number of successes divided by the total number in the sample<\/p>\n<p><strong>rational numbers:<\/strong>\u00a0fractions written as [latex]\\{\\frac{m}{n}|m\\text{ and }n\\text{ are integers and }n\\ne 0\\}[\/latex]<\/p>\n<p><strong>representative sample:<\/strong> a subset of the population that has the same characteristics as the population<\/p>\n<p><strong>sample:<\/strong> a subset of the population studied<\/p>\n<p><strong>statistic:<\/strong> a numerical characteristic of the sample; a statistic estimates the corresponding population parameter<\/p>\n<p><strong>variable:<\/strong> a characteristic of interest for each person or object in a population<\/p>\n<p><strong>whole numbers<\/strong>:\u00a0the set of natural numbers plus zero, e.g. [latex]\\{0,1,2,3,\\dots\\}[\/latex]<\/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-689\">\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>Introductory Statistics. <strong>Authored by<\/strong>: Barbara Illowsky, Susan Dean. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-key-terms\">https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-key-terms<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/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":10,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Introductory Statistics\",\"author\":\"Barbara Illowsky, Susan Dean\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-key-terms\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\"},{\"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-689","chapter","type-chapter","status-publish","hentry"],"part":23,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/689","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\/689\/revisions"}],"predecessor-version":[{"id":3348,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/689\/revisions\/3348"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/23"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/689\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=689"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=689"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=689"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}