{"id":"cb_question_bank:dfd8c207-7f10-454e-95f5-2048e4df5505","source_id":"cb_question_bank","source_item_id":"dfd8c207-7f10-454e-95f5-2048e4df5505","external_id":null,"ibn":"070909-DC","question_id":"6670e407","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.C.","skill":"One-variable data: Distributions and measures of center and spread","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The table above shows the number of students from two different high schools who completed summer internships in each of five years. No student attended both schools. Which of the following statements are true about the number of students who completed summer internships for the 5 years shown? The mean number from Foothill High School is greater than the mean number from Valley High School. The median number from Foothill High School is greater than the median number from Valley High School.","stimulus":"Number of High School Students Who Completed Summer Internships High school Year 2008 2009 2010 2011 2012 Foothill 87 80 75 76 70 Valley 44 54 65 76 82 Total 131 134 140 152 152","stimulus_html":"<div><div class=\"prose style:1 \"><div><table class=\"table_WithBorder\" style=\"width: 33%;\"><caption><span class=\"title_line passage-title\">Number of High School Students Who<br>Completed Summer Internships</span></caption><thead><tr><th colspan=\"1\" rowspan=\"2\" scope=\"col\" style=\"text-align: left; vertical-align: middle;\">High school</th><th colspan=\"5\" rowspan=\"1\" scope=\"colgroup\" style=\"text-align: center; vertical-align: middle;\">Year</th></tr><tr><th scope=\"col\" style=\"text-align: center; vertical-align: middle;\">2008</th><th scope=\"col\" style=\"text-align: center; vertical-align: middle;\">2009</th><th scope=\"col\" style=\"text-align: center; vertical-align: middle;\">2010</th><th scope=\"col\" style=\"text-align: center; vertical-align: middle;\">2011</th><th scope=\"col\" style=\"text-align: center; vertical-align: middle;\">2012</th></tr><tr></tr></thead><tbody><tr><th scope=\"row\" style=\"text-align: left; vertical-align: middle;\">Foothill</th><td style=\"text-align: center; vertical-align: middle;\">87</td><td style=\"text-align: center; vertical-align: middle;\">80</td><td style=\"text-align: center; vertical-align: middle;\">75</td><td style=\"text-align: center; vertical-align: middle;\">76</td><td style=\"text-align: center; vertical-align: middle;\">70</td></tr><tr><th scope=\"row\" style=\"text-align: left; vertical-align: middle;\">Valley</th><td style=\"text-align: center; vertical-align: middle;\">44</td><td style=\"text-align: center; vertical-align: middle;\">54</td><td style=\"text-align: center; vertical-align: middle;\">65</td><td style=\"text-align: center; vertical-align: middle;\">76</td><td style=\"text-align: center; vertical-align: middle;\">82</td></tr><tr><th scope=\"row\" style=\"text-align: center; vertical-align: middle;\">Total</th><td style=\"text-align: center; vertical-align: middle;\">131</td><td style=\"text-align: center; vertical-align: middle;\">134</td><td style=\"text-align: center; vertical-align: middle;\">140</td><td style=\"text-align: center; vertical-align: middle;\">152</td><td style=\"text-align: center; vertical-align: middle;\">152</td></tr></tbody></table></div></div></div>\n","stem_html":"<p class=\"stem_paragraph \">The table above shows the number of students from two different high schools who completed summer internships in each of five years. No student attended both schools. Which of the following statements are true about the number of students who completed summer internships for the 5 years shown?</p><ol class=\"list_upper_roman\"><li class=\"stem_paragraph \">The mean number from Foothill High School is greater than the mean number from Valley High School.</li><li class=\"stem_paragraph \">The median number from Foothill High School is greater than the median number from Valley High School.</li></ol><p></p>\n","rationale_html":"<p>Choice C is correct. The mean of a data set is found by dividing the sum of the values by the number of values. Therefore, the mean number of students who completed summer internships from Foothill High School is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/00fbdfe04f3444fb59fa5660f6adb7db5871762acc3e0a4a83af79a454e4f987\" alt=\"the fraction with numerator 87 plus 80, plus 75, plus 76, plus 70, and denominator 5, equals, the fraction 388 over 5\"></span>, or 77.6. Similarly, the mean number from Valley High School is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c1c2d3e4e36ccdd4853a1b2043983f2f5dfdf67a9c7a2c22036acd6f1b6b9284\" alt=\"the fraction with numerator 44 plus 54, plus 65, plus 76, plus 82, and denominator 5, equals, the fraction 321 over 5\"></span>, or 64.2. Thus, the mean number from Foothill High School is greater than the mean number from Valley High School. When a data set has an odd number of elements, the median can be found by ordering the values from least to greatest and determining the value in the middle. Since there are five values in each data set, the third value in each ordered list is the median. Therefore, the median number from Foothill High School is 76 and the median number from Valley High School is 65. Thus, the median number from Foothill High School is greater than the median number from Valley High School.</p><p>Choices A, B, and D are incorrect and may result from various misconceptions or miscalculations.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":true,"source_created_at":"2023-08-02T20:25:59.632000+00:00","source_updated_at":"2023-08-02T20:25:59.632000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">I only</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">II only</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">I and II</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">Neither I nor II</p>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}