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Problem-Solving and Data Analysis / One-variable data: Distributions and measures of center and spread Difficulty: Medium

Men's Height
Group	Sample size	Mean (centimeters)	Standard deviation (centimeters)
A	2,500	186	12.5
B	2,500	186	19.1

The results of two independent surveys are shown in the table below.

Which statement is true based on the table?

The Group A data set was identical to the Group B data set.

Group B contained the tallest participant.

The heights of the men in Group B had a larger spread than the heights of the men in Group A.

The median height of Group B is larger than the median height of Group A.

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Explanation

Choice C is correct. Standard deviation is a measure of spread, so data sets with larger standard deviations tend to have larger spread. The standard deviation of the heights of the men in Group B is larger than the standard deviation of the heights of the men in Group A. Therefore, the heights of the men in Group B had a larger spread than the heights of the men in Group A.

Choice A is incorrect. If two data sets are identical, they will have equivalent means and equivalent standard deviations. Since the two data sets have different standard deviations, they cannot be identical. Choice B is incorrect. Without knowing the maximum value for each data set, it’s impossible to know which group contained the tallest participant. Choice D is incorrect. Since the means of the two groups are equivalent, the medians could also be the same or could be different, but it's impossible to tell from the given information.