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One-variable data: Distributions and measures of center and spread SAT question

Math · Problem-Solving and Data Analysis · Hard · Answer it here, explanation included.

The figure presents a 2-column table, with 7 rows of data, titled “Percent of Residents Who Earned a Bachelor’s Degree or Higher.” The heading for the first column is “State,” and the heading for the second column is “Percent of residents.” The 7 rows of data are as follows. Row 1. State A; 21 point 9 percent. Row 2. State B; 27 point 9 percent. Row 3. State C; 25 point 9 percent. Row 4. State D; 19 point 5 percent. Row 5. State E; 30 point 1 percent. Row 6. State F; 36 point 4 percent. Row 7. State G; 35 point 5 percent.

A survey was given to residents of all 50 states asking if they had earned a bachelor’s degree or higher. The results from 7 of the states are given in the table above. The median percent of residents who earned a bachelor’s degree or higher for all 50 states was 26.95%. What is the difference between the median percent of residents who earned a bachelor’s degree or higher for these 7 states and the median for all 50 states?

ExplanationShow

Choice B is correct. The median of a set of numbers is the middle value of the set values when ordered from least to greatest. If the percents in the table are ordered from least to greatest, the middle value is 27.9%. The difference between 27.9% and 26.95% is 0.95%.

Choice A is incorrect and may be the result of calculation errors or not finding the median of the data in the table correctly. Choice C is incorrect and may be the result of finding the mean instead of the median. Choice D is incorrect and may be the result of using the middle value of the unordered list.

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