{"id":"cb_question_bank:70868c28-6df9-4e7d-9476-786351e0da92","source_id":"cb_question_bank","source_item_id":"70868c28-6df9-4e7d-9476-786351e0da92","external_id":null,"ibn":"027874-DC","question_id":"708590d7","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":1,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following statements correctly compares the means of data set A and data set B?","stimulus":"Data set A is the set consisting of the following seven numbers: 1 comma 2, comma 3, comma 4, comma 5, comma 6, comma 7. Data set B is the set consisting of the following seven numbers: 1 comma 1, comma 2, comma 2, comma 3, comma 3, comma 4.","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ca39e0361ed41eef028193dce2adc2e39a2ac34f7d3ad45512d8daeee463d5b5\" alt=\"Data set A is the set consisting of the following seven numbers: 1 comma 2, comma 3, comma 4, comma 5, comma 6, comma 7.\nData set B is the set consisting of the following seven numbers: 1 comma 1, comma 2, comma 2, comma 3, comma 3, comma 4.\n\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following statements correctly compares the means of data set A and data set B?</p>\n","rationale_html":"<p>Choice D is correct. The mean of a data set is found by dividing the sum of the values in the data set by the number of values in the data set. Therefore, the mean of data set A is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/aeffe1d344d654035ded0e506d53a1425d09c979b33449481b3af0fee1285d5c\" alt=\"the fraction with numerator 1 plus 2, plus 3, plus 4, plus 5, plus 6, plus 7, and denominator 7, equals, the fraction 28 over 7\"></span>, or 4. The mean of data set B is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/52cbbe038d3830bab7cc1ed380b97ed09d573b0a1e5b444554bd9d40712b7b3b\" alt=\"the fraction with numerator 1 plus 1, plus 2, plus 2, plus 3, plus 3, plus 4, and denominator 7, equals, the fraction 16 over 7\"></span>, or approximately 2.2857. Therefore, the mean of data set A is greater than the mean of data set B.</p><p>Alternate approach: Data set A and data set B are both ordered from least to greatest value. Besides the first value in each data set, which is 1, each value in ordered data set B is less than the respective value in ordered data set A. Therefore, conceptually, the mean of data set A must be greater than the mean of data set B.</p><p>Choices A, B, and C are incorrect and may result from various misconceptions or miscalculations.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.622000+00:00","source_updated_at":"2023-08-02T20:25:59.622000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">The mean of each data set is 2.</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">The mean of each data set is 4.</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">The mean of data set A is less than the mean of data set B.</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">The mean of data set A is greater than the mean of data set B.</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}}