{"id":"cb_question_bank:11036db6-9f52-456f-84ca-575ae4c42664","source_id":"cb_question_bank","source_item_id":"11036db6-9f52-456f-84ca-575ae4c42664","external_id":null,"ibn":"027703-DC","question_id":"82aaa0a1","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.D.","skill":"Two-variable data: Models and scatterplots","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Of the following, which is the best model for the data in the scatterplot?","stimulus":"The figure presents a scatterplot in the x y plane. The numbers 0 through 6, in increments of 1, are indicated on the x axis. The numbers 0 through 20, in increments of 2, are indicated on the y axis. There are 12 data points in the scatterplot. The data points are in the shape of a parabola that opens upward. The data points begin on the y axis at 20, and trend downward and to the right until they reach a first low point with coordinates 2 point 5 comma 5 and a second low point with coordinates 3 comma 5. Then the data points trend upward and to the right until they reach the last point with coordinates 5 point 5 comma 20.","stimulus_html":"<div class=\"stimulus_reference \">\n\t<div class=\"standalone_image \"><img src=\"/api/assets/aec46b9dbf6d5da97c19595e4100ea8de1ea567d3b8bea31ab36eb871c88cb12\" alt=\"The figure presents a scatterplot in the x y plane. The numbers 0 through 6, in increments of 1, are indicated on the x axis. The numbers 0 through 20, in increments of 2, are indicated on the y axis. There are 12 data points in the scatterplot. The data points are in the shape of a parabola that opens upward. The data points begin on the y axis at 20, and trend downward and to the right until they reach a first low point with coordinates 2 point 5 comma 5 and a second low point with coordinates 3 comma 5.  Then the data points trend upward and to the right until they reach the last point with coordinates 5 point 5 comma 20.\" width=\"155\" height=\"161\"></div>\n</div>\n","stem_html":"<p class=\"stem_paragraph \">Of the following, which is the best model for the data in the scatterplot?</p>\n","rationale_html":"<p>Choice B is correct. The graphical model that most closely fits the data in the scatterplot is a model in which the number of data points above and below the model are approximately balanced. Fitting a graphical model to the data shown results in an upward-facing parabola with a <span class=\"italic\">y</span>-intercept near <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f64f1d55b9ec3ab92cacb3c0b904567cd1591f539fcacd7c6d5665bdb2d469e6\" alt=\"the point with coordinates 0 comma 20 \"></span> and a vertex with an approximate <span class=\"italic\">x-</span>value of 2.5. Of the given choices, only choice B gives an equation of an upward-facing parabola with a <span class=\"italic\">y</span>-intercept at <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f64f1d55b9ec3ab92cacb3c0b904567cd1591f539fcacd7c6d5665bdb2d469e6\" alt=\"the point with coordinates 0 comma 20 \"></span>. Furthermore, substituting 2.5 for <span class=\"italic\">x</span> into the equation in choice B yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9f82c1a6f2626e5235d495170f4c7f7c58a2498e80346cd72371855d50bcd092\" alt=\"y equals 5\"></span>. This is approximately the <span class=\"italic\">y</span>-value of the vertex of the model.</p><p>Choices A, C, and D are incorrect. These equations don’t give a graphical model that best fits the data. At <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/37b98ea685bc6992d8e8e7df92ac8c58c1621b437bc601cc6767a21168bc15e0\" alt=\"x equals 0\"></span>, they have <span class=\"italic\">y</span>-values of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9c9ceecdd845d666c89f63289b2057c50b70fc985000b67442aa58f2fad36303\" alt=\"negative 20\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b62558094601a23d6fe95ffbc037ca0c41dd10264b6e51f4163b9ed575c135a3\" alt=\"negative 3\"></span>, and 3, respectively. At <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/886c6442d4ffe3dd4ce12715346cb6cce71381a93a23cbccf890465c9666971d\" alt=\"x equals 2 point 5\"></span>, they have <span class=\"italic\">y</span>-values of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ce88aaee31e578998c72151cf9523ad3a4f83964274bb703dc990d365f0dc8b7\" alt=\"negative 35\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b62558094601a23d6fe95ffbc037ca0c41dd10264b6e51f4163b9ed575c135a3\" alt=\"negative 3\"></span>, and 3, respectively.</p><p>&nbsp;</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.621000+00:00","source_updated_at":"2023-08-02T20:25:59.621000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d3c21a5ec090537e8dd6492d3aa6a4b3dfb563438bc154725452aa4559559edf\" alt=\"y equals, 2 x squared, minus 11 x, minus 20\"></span></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5fa257d26e3f6a1731c63741e4b4c4ced976e9141495b2c2bc739b069b27b85a\" alt=\"y equals, 2 x squared, minus 11 x, plus 20\"></span></span></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/19589e844b1140b9c6ae04cd1d7bb8f0356b67ca6612c14df12d5fe0dae88f6e\" alt=\"y equals, 2 x squared, minus 5 x, minus 3\"></span></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f25768cb025f8f4e8e539673ed0c1096dd9ce93bc1c8ba0ea471c2f3da24e66b\" alt=\"y equals, 2 x squared, minus 5 x, plus 3\"></span></span></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}}