{"id":"cb_question_bank:971ac238-5160-450a-8dbb-f7005873c331","source_id":"cb_question_bank","source_item_id":"971ac238-5160-450a-8dbb-f7005873c331","external_id":"f1db57ba-417f-4c96-ae7e-80f171f39606","ibn":null,"question_id":"4626102e","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":"The data for the dot plot are as follows: 22: 5 dots 23: 4 dots 24: 3 dots 25: 2 dots 26: 1 dot The dot plot represents the 15 values in data set A. Data set B is created by adding 56 to each of the values in data set A. Which of the following correctly compares the medians and the ranges of data sets A and B?","stimulus":"","stimulus_html":null,"stem_html":"

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The dot plot represents the 15\n values in data set A. Data set B is created by adding 56\n to each of the values in data set A. Which of the following correctly compares the medians and the ranges of data sets A and B?

","rationale_html":"

Choice C is correct. The median of a data set with an odd number of values, in ascending or descending order, is the middle value of the data set, and the range of a data set is the positive difference between the maximum and minimum values in the data set. Since the dot plot shown gives the values in data set A in ascending order and there are 15\n values in the data set, the eighth value in data set A, 23\n, is the median. The maximum value in data set A is 26\n and the minimum value is 22\n, so the range of data set A is 26-22, or 4\n. It’s given that data set B is created by adding 56\n to each of the values in data set A. Increasing each of the 15\n values in data set A by 56\n will also increase its median value by 56\n making the median of data set B 79\n. Increasing each value of data set A by 56\n does not change the range, since the maximum value of data set B is 26+56, or 82\n, and the minimum value is 22+56, or 78\n, making the range of data set B 82-78, or 4\n. Therefore, the median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A.

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

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

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

","correct_answer":["C"],"has_media":true,"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":"

The median of data set B is equal to the median of data set A, and the range of data set B is equal to the range of data set A.

","ord":0},{"label":"B","content_html":"

The median of data set B is equal to the median of data set A, and the range of data set B is greater than the range of data set A.

","ord":1},{"label":"C","content_html":"

The median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A.

","ord":2},{"label":"D","content_html":"

The median of data set B is greater than the median of data set A, and the range of data set B is greater than the range of data set A.

","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}}