{"id":"cb_question_bank:70a2dae4-5561-4925-8451-eaa41184d744","source_id":"cb_question_bank","source_item_id":"70a2dae4-5561-4925-8451-eaa41184d744","external_id":"32297287-d739-4961-acc3-2eed761e3e0d","ibn":null,"question_id":"bf47ad54","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":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Each of the following frequency tables represents a data set. Which data set has the greatest mean?","stimulus":"","stimulus_html":null,"stem_html":"

Each of the following frequency tables represents a data set. Which data set has the greatest mean?

","rationale_html":"

Choice A is correct. The tables in choices B, C, and D each represent a data set where the values 80\n and 90\n have the same frequency and the values 70\n and 100\n have the same frequency. It follows that each of these data sets is symmetric around the value halfway between 80\n and 90\n, or 85\n. When a data set is symmetric around a value, that value is the mean of the data set. Therefore, the data sets represented by the tables in choices B, C, and D each have a mean of 85\n. The table in choice A represents a data set where the value 90\n has a greater frequency than the value 80\n and the value 100\n has a greater frequency than the value 70\n. It follows that this data set has a mean greater than 85\n. Therefore, of the given choices, choice A represents the data set with the greatest mean.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":true,"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":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ValueFrequency
70\n4\n
80\n5\n
90\n6\n
100\n7\n
","ord":0},{"label":"B","content_html":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ValueFrequency
70\n6\n
80\n6\n
90\n6\n
100\n6\n
","ord":1},{"label":"C","content_html":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ValueFrequency
70\n7\n
80\n6\n
90\n6\n
100\n7\n
","ord":2},{"label":"D","content_html":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ValueFrequency
70\n8\n
80\n5\n
90\n5\n
100\n8\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}}