{"id":3908,"date":"2022-03-16T17:50:28","date_gmt":"2022-03-16T17:50:28","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=3908"},"modified":"2022-03-17T05:24:28","modified_gmt":"2022-03-17T05:24:28","slug":"instructor-guide-corequisite-support-five-number-summary-in-boxplots-and-datasets","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/instructor-guide-corequisite-support-five-number-summary-in-boxplots-and-datasets\/","title":{"raw":"Instructor Guide Five Number Summary in Boxplots and Datasets: Corequisite Support","rendered":"Instructor Guide Five Number Summary in Boxplots and Datasets: Corequisite Support"},"content":{"raw":"While this support activity is designed for a face-to-face, synchronous delivery, it should be noted that supporting text and interactive examples have been embedded in the digital assignment page to assist asynchronous or hybrid course delivery and to be made more accessible to students performing make-up work.<\/em>\r\n

Suggested instructional plan for synchronous active-learning<\/h2>\r\nUse this corequisite support activity to prepare students for interpreting and comparing\u00a0boxplots. The next preview assignment and in-class activity presume an understanding\u00a0of the five-number summary and what it tells us about a dataset.\u00a0Have students work in pairs or small groups throughout this support activity.\u00a0Question 1 is meant to introduce the idea of outliers informally. Give pairs or groups\u00a0time to formulate their answers, and then have a few volunteers share their answers.\u00a0Students will probably identify Japan and the United States as \u201cunusual.\u201d Hopefully,\u00a0there will be some questions as to whether Japan is an outlier. Use this gray area as an\u00a0opportunity to motivate students to engage in the support activity; the point of the\u00a0activity is to begin to understand which values are considered unusual in a statistical\u00a0sense. Let students know that they will revisit this question at the end of the support\u00a0activity.\r\n\r\nHave students continue working in pairs or small groups to answer Questions 2\u201311. The\u00a0goal of these questions is to introduce the idea of quartiles and the five-number\u00a0summary. Use Question 5 to gauge students\u2019 understanding of median, and then hold a\u00a0brief check-in with the whole class after Question 11 to ensure students\u2019 understanding\u00a0of quartiles. If time permits, have a few students summarize quartiles and the idea of the\u00a0five-number summary.\r\n\r\nThe goal of Questions 12 and 13 is to introduce the interquartile range (IQR). The IQR will be\u00a0used in the preview assignment to determine values that are outliers. The focus in this\u00a0support activity is on the procedural fluency required to compute the interquartile range.\u00a0However, depending on how quickly students move through this support activity, you\u00a0can apply the IQR to determine if Japan and the United States are outliers in a\u00a0statistical sense. See the optional extension below.\r\n\r\nUse Question 14 as a way to launch a discussion. Highlight the idea that some outliers\u00a0seem quite simple to spot (such as the GDP per capita of the United States), but others\u00a0are harder to identify (such as Japan\u2019s GDP per capita). Prompt students to come up\u00a0with their own rules for determining outliers. This discussion is an opportunity to interject\u00a0the idea that statistics is a field that requires interpretation. The study of quantitative\u00a0data does not imply certainty or lack subtlety. Students will learn a formal method for\u00a0determining which values are outliers in the preview assignment.\r\n\r\nOptional Extension<\/strong>:\u00a0If time permits, discuss elements of this article: https:\/\/towardsdatascience.com\/why-1-5-in-iqr-method-of-outlier-detection-5d07fdc82097<\/a>. Have students compute 1.5(IQR)\u00a0and determine if Japan is an outlier.\r\n\r\nNote that students are given the task above to computer 1.5(IQR) to determine if Japan is an outlier, with a discussion but without the article linked, in the final Interactive Example in the digital activity page. This is done to facilitate asynchronous or hybrid delivery and to accommodate students working alone on the activity.<\/em>","rendered":"

While this support activity is designed for a face-to-face, synchronous delivery, it should be noted that supporting text and interactive examples have been embedded in the digital assignment page to assist asynchronous or hybrid course delivery and to be made more accessible to students performing make-up work.<\/em><\/p>\n

Suggested instructional plan for synchronous active-learning<\/h2>\n

Use this corequisite support activity to prepare students for interpreting and comparing\u00a0boxplots. The next preview assignment and in-class activity presume an understanding\u00a0of the five-number summary and what it tells us about a dataset.\u00a0Have students work in pairs or small groups throughout this support activity.\u00a0Question 1 is meant to introduce the idea of outliers informally. Give pairs or groups\u00a0time to formulate their answers, and then have a few volunteers share their answers.\u00a0Students will probably identify Japan and the United States as \u201cunusual.\u201d Hopefully,\u00a0there will be some questions as to whether Japan is an outlier. Use this gray area as an\u00a0opportunity to motivate students to engage in the support activity; the point of the\u00a0activity is to begin to understand which values are considered unusual in a statistical\u00a0sense. Let students know that they will revisit this question at the end of the support\u00a0activity.<\/p>\n

Have students continue working in pairs or small groups to answer Questions 2\u201311. The\u00a0goal of these questions is to introduce the idea of quartiles and the five-number\u00a0summary. Use Question 5 to gauge students\u2019 understanding of median, and then hold a\u00a0brief check-in with the whole class after Question 11 to ensure students\u2019 understanding\u00a0of quartiles. If time permits, have a few students summarize quartiles and the idea of the\u00a0five-number summary.<\/p>\n

The goal of Questions 12 and 13 is to introduce the interquartile range (IQR). The IQR will be\u00a0used in the preview assignment to determine values that are outliers. The focus in this\u00a0support activity is on the procedural fluency required to compute the interquartile range.\u00a0However, depending on how quickly students move through this support activity, you\u00a0can apply the IQR to determine if Japan and the United States are outliers in a\u00a0statistical sense. See the optional extension below.<\/p>\n

Use Question 14 as a way to launch a discussion. Highlight the idea that some outliers\u00a0seem quite simple to spot (such as the GDP per capita of the United States), but others\u00a0are harder to identify (such as Japan\u2019s GDP per capita). Prompt students to come up\u00a0with their own rules for determining outliers. This discussion is an opportunity to interject\u00a0the idea that statistics is a field that requires interpretation. The study of quantitative\u00a0data does not imply certainty or lack subtlety. Students will learn a formal method for\u00a0determining which values are outliers in the preview assignment.<\/p>\n

Optional Extension<\/strong>:\u00a0If time permits, discuss elements of this article: https:\/\/towardsdatascience.com\/why-1-5-in-iqr-method-of-outlier-detection-5d07fdc82097<\/a>. Have students compute 1.5(IQR)\u00a0and determine if Japan is an outlier.<\/p>\n

Note that students are given the task above to computer 1.5(IQR) to determine if Japan is an outlier, with a discussion but without the article linked, in the final Interactive Example in the digital activity page. This is done to facilitate asynchronous or hybrid delivery and to accommodate students working alone on the activity.<\/em><\/p>\n","protected":false},"author":25777,"menu_order":17,"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-3908","chapter","type-chapter","status-publish","hentry"],"part":3890,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3908","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\/25777"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3908\/revisions"}],"predecessor-version":[{"id":4083,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3908\/revisions\/4083"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/3890"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3908\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=3908"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=3908"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=3908"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=3908"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}