{"id":"cb_question_bank:2d9a050c-7de8-47ac-8e5a-675fc0e70a30","source_id":"cb_question_bank","source_item_id":"2d9a050c-7de8-47ac-8e5a-675fc0e70a30","external_id":"45c46b40-e7e6-4f3e-bbb1-22e0862c3911","ibn":null,"question_id":"c178d4da","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":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Value Data set A frequency Data set B frequency 30 2 9 34 4 7 38 5 5 42 7 4 46 9 2 Data set A and data set B each consist of 27 values. The table shows the frequencies of the values for each data set. Which of the following statements best compares the means of the two data sets?","stimulus":"","stimulus_html":null,"stem_html":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ValueData set A frequencyData set B frequency
30\n2\n9\n
34\n4\n7\n
38\n5\n5\n
42\n7\n4\n
46\n9\n2\n
\n

Data set A and data set B each consist of 27\n values. The table shows the frequencies of the values for each data set. Which of the following statements best compares the means of the two data sets?

","rationale_html":"

Choice A is correct. The mean value of a data set is the sum of the values of the data set divided by the number of values in the data set. When a data set is represented in a frequency table, the sum of the values in the data set is the sum of the products of each value and its frequency. For data set A, the sum of products of each value and its frequency is 302+344+385+427+469, or 1,094. It's given that there are 27\n values in data set A. Therefore, the mean of data set A is 1,09427, or approximately 40.52. Similarly, the mean of data B is 95827, or approximately 35.48. Therefore, the mean of data set A is greater than the mean of data set B.

\n

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

\n

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

\n

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

","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":true,"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 mean of data set A is greater than the mean of data set B.

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

The mean of data set A is less than the mean of data set B.

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

The mean of data set A is equal to the mean of data set B.

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

There is not enough information to compare the means of the data sets.

","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}}