{"id":"cb_question_bank:40be99bc-5b6a-4dd7-b23a-535891a0502a","source_id":"cb_question_bank","source_item_id":"40be99bc-5b6a-4dd7-b23a-535891a0502a","external_id":"bb8df1b9-8ab9-42bb-8b7f-adec3639c7f8","ibn":null,"question_id":"d65b9a87","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":"The dot plots represent the distributions of values in data sets A and B. For the dot plot titled Data Set A: The number line ranges from 10 to 16 in increments of 1. The data for the dot plot are as follows: 10: 1 dot 11: 4 dots 12: 2 dots 13: 3 dots 14: 2 dots 15: 4 dots 16: 1 dot For the dot plot titled Data Set B: The number line ranges from 10 to 16 in increments of 1. The data for the dot plot are as follows: 10: 2 dots 11: 4 dots 12: 2 dots 13: 1 dot 14: 2 dots 15: 4 dots 16: 2 dots Which of the following statements must be true? The median of data set A is equal to the median of data set B. The standard deviation of data set A is equal to the standard deviation of data set B.","stimulus":"","stimulus_html":null,"stem_html":"

The dot plots represent the distributions of values in data sets A and B.

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Which of the following statements must be true?

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    \n
  1. The median of data set A is equal to the median of data set B.
    2. \n
  2. The standard deviation of data set A is equal to the standard deviation of data set B.
    3. \n
","rationale_html":"

Choice A is correct. The median of a data set with an odd number of values that are in ascending or descending order is the middle value of the data set. Since the distribution of the values of both data set A and data set B form symmetric dot plots, and each data set has an odd number of values, it follows that the median is given by the middle value in each of the dot plots. Thus, the median of data set A is 13\n, and the median of data set B is 13\n. Therefore, statement I is true. Data set A and data set B have the same frequency for each of the values 11\n, 12\n, 14\n, and 15\n. Data set A has a frequency of 1\n for values 10\n and 16\n, whereas data set B has a frequency of 2\n for values 10\n and 16\n. Standard deviation is a measure of the spread of a data set; it is larger when there are more values further from the mean, and smaller when there are more values closer to the mean. Since both distributions are symmetric with an odd number of values, the mean of each data set is equal to its median. Thus, each data set has a mean of 13\n. Since more of the values in data set A are closer to 13\n than data set B, it follows that data set A has a smaller standard deviation than data set B. Thus, statement II is false. Therefore, only statement I must be true.

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

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Choice C 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":["A"],"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":"

I only

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

II only

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

I and II

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

Neither I nor II

","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}}