{"id":"cb_question_bank:dc8b489d-5526-4d15-824c-dfa1e20cc54c","source_id":"cb_question_bank","source_item_id":"dc8b489d-5526-4d15-824c-dfa1e20cc54c","external_id":null,"ibn":"070627-DC","question_id":"54d93874","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":6,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Andrew and Maria each collected six rocks, and the masses of the rocks are shown in the table above. The mean of the masses of the rocks Maria collected is 0.1 kilogram greater than the mean of the masses of the rocks Andrew collected. What is the value of x ?","stimulus":"Masses (kilograms) Andrew 2.4 2.5 3.6 3.1 2.5 2.7 Maria x 3.1 2.7 2.9 3.3 2.8","stimulus_html":"<div class=\"stimulus_reference\"><table border=\"1\" class=\"table_WithBorder tcp-04352d54-f756-42b1-8c91-3d4cec990526\" style=\"width: 25%;\"><thead><tr><td>&nbsp;</td><th class=\"tcp-457b0ee6-5ea4-46ba-9687-b7b086770775\" colspan=\"6\" rowspan=\"1\" scope=\"col\" style=\"text-align: center;\">Masses (kilograms)</th></tr></thead><tbody><tr><th class=\"tcp-64a12a71-da41-47a6-828c-08daee4a11d2\" scope=\"row\">Andrew</th><td class=\"tcp-23446c86-f6f7-4e7f-9a93-4788fd0b00cf\">2.4</td><td class=\"tcp-e0d47ae2-86da-4a90-9f5d-a8e1abf140bf\">2.5</td><td class=\"tcp-d4534fa6-5f94-4a98-a2c3-6f789a5e3a16\">3.6</td><td class=\"tcp-c3c394e1-a628-415e-ac8e-4e6260b4004b\">3.1</td><td class=\"tcp-076afc32-c49a-4086-abe2-6719c0e1066a\">2.5</td><td class=\"tcp-1c38a68a-d63c-4518-a1b2-4d14a157345d\">2.7</td></tr><tr><th class=\"tcp-32b40932-24ce-4d97-93e0-eb07b20418f1\" scope=\"row\">Maria</th><td class=\"tcp-52e15647-45ef-447b-a9a3-d4e41ca7ea1a\"><span class=\"italic\">x</span></td><td class=\"tcp-a103a1b3-22fe-4dbd-93c4-808b514c2ccf\">3.1</td><td class=\"tcp-5c3b1036-c6e1-44e8-90c3-b34e58a65aff\">2.7</td><td class=\"tcp-90e9f7f8-50c5-4eed-b08d-56f662e872e5\">2.9</td><td class=\"tcp-2e42d753-3b4c-4248-88cd-ed08518b7ed1\">3.3</td><td class=\"tcp-fc2b2b50-c789-4548-ab89-cfdb9187c762\">2.8</td></tr></tbody></table><div id=\"level-access-access-assistant-highlight-container\">&nbsp;</div></div>\n","stem_html":"<p class=\"stem_paragraph \">Andrew and Maria each collected six rocks, and the masses of the rocks are shown in the table above. The mean of the masses of the rocks Maria collected is 0.1 kilogram greater than the mean of the masses of the rocks Andrew collected. What is the value of <span class=\"italic\">x</span> ?</p>\n","rationale_html":"<p>The correct answer is 2.6. Since the mean of a set of numbers can be found by adding the numbers together and dividing by how many numbers there are in the set, the mean mass, in kilograms, of the rocks Andrew collected is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8fb00b09a57b3dbf69da0b270db2fbd08e8548b6599738457071e1d08b8b0d74\" alt=\"the fraction with numerator 2 point 4, plus 2 point 5, plus 3 point 6, plus 3 point 1, plus 2 point 5, plus 2 point 7, and denominator 6, equals 16 point 8 over 6.\"></span>, or 2.8. Since the mean mass of the rocks Maria collected is 0.1 kilogram greater than the mean mass of rocks Andrew collected, the mean mass of the rocks Maria collected is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/443ddd132805d3ea4e4c615f687393e4a2142e6552a9399c4a282c64ad96a617\" alt=\"2 point 8, plus 0 point 1, equals 2 point 9\"></span> kilograms. The value of <span class=\"italic\">x</span> can be found by writing an equation for finding the mean:&nbsp;<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/166dbad516a15c20dba1e8805ae9469226b68c5d747ac9a33653b7b80d6ae0bd\" alt=\"the fraction with numerator x plus 3 point 1, plus 2 point 7, plus 2 point 9, plus 3 point 3, plus 2 point 8, and denominator 6, equals 2 point 9\"></span>. Solving this equation gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d38018968b3d622974b8f2881524d0ce4538af41774cc4d684cee1d4c20f6bf7\" alt=\"x equals 2 point 6\"></span>. Note that 2.6 and 13/5 are examples of ways to enter a correct answer.</p><p>&nbsp;</p><div id=\"level-access-access-assistant-highlight-container\">&nbsp;</div><p></p>\n","correct_answer":["2.6"],"has_media":true,"has_mathml":false,"has_table":true,"source_created_at":"2023-08-02T20:25:59.631000+00:00","source_updated_at":"2023-08-02T20:25:59.631000+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}}