{"id":"cb_practice_pdf:t11-math-m2-q25","source_id":"cb_practice_pdf","source_item_id":"t11-math-m2-q25","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-11","module_number":2,"position":25,"stem":"25 The histogram summarizes data set A, which represents the number of points per player earned by 50 players of a game. A new player earns 18 points playing the game, and this number of points is added to data set A to create data set B with 51 values. Which of the following must be true? I. The median number of points per player for data set B is less than the median number of points per player for data set A. II. The mean number of points per player for data set B is less than the mean number of points per player for data set A.","stimulus":"","stimulus_html":null,"stem_html":"<p>25 The histogram summarizes data set A, which represents the number of points per player earned by 50 players of a game. A new player earns 18 points playing the game, and this number of points is added to data set A to create data set B with 51 values. Which of the following must be true? I. The median number of points per player for data set B is less than the median number of points per player for data set A. II. The mean number of points per player for data set B is less than the mean number of points per player for data set A.</p>","rationale_html":"<p>Choice B is correct. The mean of a data set is the sum of the values divided by the 18 number of values. It’s given that a new player earns points playing the game, and this number of points is added to data set A to create data set B with 51 values. The histogram shows that all the values in data set A are greater than 18 18 . Since the additional number of points, , is less than any of the values in the original data set, the mean number of points per player for data set B is less than the mean number of points per player for data set A. The median of a data set with 50 25th 26th values is between the and values when the values are listed in 51 26th ascending order. The median of a data set with values is the value when the values are listed in ascending order. Therefore, the median of data set B is the 26th 25th value in data set B, which is the value in data set A. The histogram 25th 26th 50 shows that the and values in data set A are both between and 60 25th 26th points. Therefore, the and values in data set A could be equal, in 25th 26th which case the median of data set A would be equal to both the and values in data set A. Then, the median number of points per player for data set A would be equal to the median number of points per player for data set B. Therefore, only statement II must be true. Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["B"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>I only</p>","ord":0},{"label":"B","content_html":"<p>II only</p>","ord":1},{"label":"C","content_html":"<p>I and II</p>","ord":2},{"label":"D","content_html":"<p>Neither I nor II</p>","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}