{"id":1032,"date":"2022-01-11T22:41:58","date_gmt":"2022-01-11T22:41:58","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=1032"},"modified":"2022-02-04T21:55:38","modified_gmt":"2022-02-04T21:55:38","slug":"4e","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/4e\/","title":{"raw":"4E","rendered":"4E"},"content":{"raw":"
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Skill or Concept: I can . . .<\/td>\r\nQuestions to check your understanding<\/td>\r\nRating\r\nfrom 1 to 5<\/td>\r\n<\/tr>\r\n
Convert values into standardized scores.<\/td>\r\n1\u20134<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Use a value\u2019s standardized score to determine whether the value is above, below, or equal to the mean.<\/td>\r\n4<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Explain the Empirical Rule.<\/td>\r\n5<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Two \"A\r\n\r\nGlossary\r\n
\r\n \t
standardized value<\/dt>\r\n \t
the number of standard deviations an observation is away from the mean. Also referred to as a\u00a0z-score<\/strong>.<\/dd>\r\n<\/dl>\r\n
\r\n \t
Empirical Rule<\/dt>\r\n \t
a guideline that predicts the percentage of observations within a certain number of standard deviations. Also known as the\u00a068-95-99.7 Rule<\/strong>\u00a0which states that\u00a0in a bell-shaped, unimodal distribution, almost all of the observed data values,\u00a0x<\/span><\/span><\/span><\/span>x<\/mi><\/math><\/span><\/span>, lie within three standard deviations,\u00a0\u03c3<\/span><\/span><\/span><\/span>\u03c3<\/mi><\/math><\/span><\/span>, to either side of the mean,\u00a0\u03bc<\/span><\/span><\/span><\/span>\u03bc<\/mi><\/math><\/span><\/span>. More specifically, about 68% of observations in a dataset will be within one standard deviation of the mean\u00a0(<\/span><\/span>\u03bc<\/span><\/span>\u00b1<\/span><\/span>\u03c3<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>(<\/mo>\u03bc<\/mi>\u00b1<\/mo>\u03c3<\/mi><\/mrow>)<\/mo><\/mrow><\/math><\/span><\/span>,\u00a0about 95% of the observations in a dataset will be within two standard deviations of the mean\u00a0(<\/span><\/span>\u03bc<\/span><\/span>\u00b1<\/span><\/span>2<\/span><\/span>\u03c3<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>(<\/mo>\u03bc<\/mi>\u00b1<\/mo>2<\/mn>\u03c3<\/mi><\/mrow>)<\/mo><\/mrow><\/math><\/span><\/span>, and\u00a0about 99.7% of the observations in a dataset will be within three standard deviations of the mean\u00a0(<\/span><\/span>\u03bc<\/span><\/span>\u00b1<\/span><\/span>3<\/span><\/span>\u03c3<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>(<\/mo>\u03bc<\/mi>\u00b1<\/mo>3<\/mn>\u03c3<\/mi><\/mrow>)<\/mo><\/mrow><\/math><\/span><\/span>.<\/dd>\r\n<\/dl>\r\n<\/div>","rendered":"
\n\n\n\n\n\n\n
Skill or Concept: I can . . .<\/td>\nQuestions to check your understanding<\/td>\nRating
\nfrom 1 to 5<\/td>\n<\/tr>\n
Convert values into standardized scores.<\/td>\n1\u20134<\/td>\n<\/td>\n<\/tr>\n
Use a value\u2019s standardized score to determine whether the value is above, below, or equal to the mean.<\/td>\n4<\/td>\n<\/td>\n<\/tr>\n
Explain the Empirical Rule.<\/td>\n5<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"Two \"A<\/p>\n

Glossary<\/p>\n

\n
standardized value<\/dt>\n
the number of standard deviations an observation is away from the mean. Also referred to as a\u00a0z-score<\/strong>.<\/dd>\n<\/dl>\n
\n
Empirical Rule<\/dt>\n
a guideline that predicts the percentage of observations within a certain number of standard deviations. Also known as the\u00a068-95-99.7 Rule<\/strong>\u00a0which states that\u00a0in a bell-shaped, unimodal distribution, almost all of the observed data values,\u00a0x<\/span><\/span><\/span><\/span>x<\/mi><\/math><\/span><\/span>, lie within three standard deviations,\u00a0\u03c3<\/span><\/span><\/span><\/span>\u03c3<\/mi><\/math><\/span><\/span>, to either side of the mean,\u00a0\u03bc<\/span><\/span><\/span><\/span>\u03bc<\/mi><\/math><\/span><\/span>. More specifically, about 68% of observations in a dataset will be within one standard deviation of the mean\u00a0(<\/span><\/span>\u03bc<\/span><\/span>\u00b1<\/span><\/span>\u03c3<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>(<\/mo>\u03bc<\/mi>\u00b1<\/mo>\u03c3<\/mi><\/mrow>)<\/mo><\/mrow><\/math><\/span><\/span>,\u00a0about 95% of the observations in a dataset will be within two standard deviations of the mean\u00a0(<\/span><\/span>\u03bc<\/span><\/span>\u00b1<\/span><\/span>2<\/span><\/span>\u03c3<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>(<\/mo>\u03bc<\/mi>\u00b1<\/mo>2<\/mn>\u03c3<\/mi><\/mrow>)<\/mo><\/mrow><\/math><\/span><\/span>, and\u00a0about 99.7% of the observations in a dataset will be within three standard deviations of the mean\u00a0(<\/span><\/span>\u03bc<\/span><\/span>\u00b1<\/span><\/span>3<\/span><\/span>\u03c3<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>(<\/mo>\u03bc<\/mi>\u00b1<\/mo>3<\/mn>\u03c3<\/mi><\/mrow>)<\/mo><\/mrow><\/math><\/span><\/span>.<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":23592,"menu_order":10,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1032","chapter","type-chapter","status-publish","hentry"],"part":704,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1032","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1032\/revisions"}],"predecessor-version":[{"id":2810,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1032\/revisions\/2810"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/704"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1032\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=1032"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=1032"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=1032"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=1032"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}