{"id":"cb_question_bank:b8fe154b-37b8-4187-863c-dd1005243c95","source_id":"cb_question_bank","source_item_id":"b8fe154b-37b8-4187-863c-dd1005243c95","external_id":"4135b77c-4178-4cdc-8f4a-8f46e634b934","ibn":null,"question_id":"391ae4b2","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":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Data set F consists of 55 integers between 170 and 290 . Data set G consists of all the integers in data set F as well as the integer 10 . Which of the following must be less for data set F than for data set G? The mean The median","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Data set F consists of <math alttext=\"55\"><mn>55</mn>\n</math> integers between <math alttext=\"170\"><mn>170</mn>\n</math> and <math alttext=\"290\"><mn>290</mn>\n</math>. Data set G consists of all the integers in data set F as well as the integer <math alttext=\"10\"><mn>10</mn>\n</math>. Which of the following must be less for data set F than for data set G?</p>\n<ol style=\"list-style-type: upper-roman;\">\n<li style=\"text-align: left;\">The mean</li>\n<li style=\"text-align: left;\">The median</li>\n</ol>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. It's given that data set F consists of <math alttext=\"55\"><mn>55</mn>\n</math> integers between <math alttext=\"170\"><mn>170</mn>\n</math> and <math alttext=\"290\"><mn>290</mn>\n</math> and data set G consists of all the integers in data set F as well as the integer <math alttext=\"10\"><mn>10</mn>\n</math>. Since the integer <math alttext=\"10\"><mn>10</mn>\n</math> is less than all the integers in data set F, the mean of data set G must be less than the mean of data set F. Thus, the mean of data set F isn't less than the mean of data set G. When a data set is in ascending order, the median is between the two middle values when there is an even number of values and the median is the middle value when there is an odd number of values. It follows that the median of data set F is either greater than or equal to the median of data set G. Therefore, the median of data set F isn't less than the median of data set G. Thus, neither the mean nor the median must be less for data set F than for data set G.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.833000+00:00","source_updated_at":"2023-08-02T20:25:59.833000+00:00","options":[{"label":"A","content_html":"<p style=\"text-align: left;\">I only</p>","ord":0},{"label":"B","content_html":"<p style=\"text-align: left;\">II only</p>","ord":1},{"label":"C","content_html":"<p style=\"text-align: left;\">I and II</p>","ord":2},{"label":"D","content_html":"<p style=\"text-align: left;\">Neither I nor II</p>","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}}