{"id":"cb_question_bank:b7e46c87-38b5-4762-8ff1-2d83ff1f2d8d","source_id":"cb_question_bank","source_item_id":"b7e46c87-38b5-4762-8ff1-2d83ff1f2d8d","external_id":"b9761b18-7942-4214-89a5-1726fe26fe75","ibn":null,"question_id":"98958ae8","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":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Data set A consists of the heights of 75 objects and has a mean of 25 meters. Data set B consists of the heights of 50 objects and has a mean of 65 meters. Data set C consists of the heights of the 125 objects from data sets A and B. What is the mean, in meters, of data set C?","stimulus":"","stimulus_html":null,"stem_html":"

Data set A consists of the heights of 75\n objects and has a mean of 25\n meters. Data set B consists of the heights of 50\n objects and has a mean of 65\n meters. Data set C consists of the heights of the 125\n objects from data sets A and B. What is the mean, in meters, of data set C?

","rationale_html":"

The correct answer is 41\n. The mean of a data set is computed by dividing the sum of the values in the data set by the number of values in the data set. It’s given that data set A consists of the heights of 75\n objects and has a mean of 25\n meters. This can be represented by the equation \n\t\n\t\t\n\t\t\tx\n\t\t\t75\n\t\t\n\t\n\t=\n\t25\n\n, where x\n represents the sum of the heights of the objects, in meters, in data set A. Multiplying both sides of this equation by 75\n yields x=7525, or \n\tx\n\t=\n\t1,875\n\n meters. Therefore, the sum of the heights of the objects in data set A is 1,875\n meters. It’s also given that data set B consists of the heights of 50\n objects and has a mean of 65\n meters. This can be represented by the equation \n\t\n\t\t\n\t\t\ty\n\t\t\t50\n\t\t\n\t\n\t=\n\t65\n\n, where y\n represents the sum of the heights of the objects, in meters, in data set B. Multiplying both sides of this equation by 50\n yields y=5065, or \n\ty\n\t=\n\t3,250\n\n meters. Therefore, the sum of the heights of the objects in data set B is 3,250\n meters. Since it’s given that data set C consists of the heights of the 125\n objects from data sets A and B, it follows that the mean of data set C is the sum of the heights of the objects, in meters, in data sets A and B divided by the number of objects represented in data sets A and B, or 1,875+3,250125, which is equivalent to 41\n meters. Therefore, the mean, in meters, of data set C is 41\n.

","correct_answer":["41"],"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":[],"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}}