ACT Math · Statistics and data analysis
Group A has a median of 60 and an IQR of 10. Group B has a median of 75 and an IQR of 20. Which group shows more variability in its middle…
Group A has a median of 60 and an IQR of 10. Group B has a median of 75 and an IQR of 20. Which group shows more variability in its middle 50% of data?
Answer and explanation
Answer: B: Group B
The interquartile range measures the spread of the middle of the data. Group A has an IQR of and Group B has an IQR of , so Group B's middle half is more spread out, choice B. The medians describe the centers of the groups and have no bearing on the spread, so the fact that Group B's median is higher does not matter. Choice A reverses the comparison. Choice C is wrong because the IQRs differ. Choice D is wrong because the IQR is exactly the measure of middle-half variability that the question asks for.
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