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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.

Each of the following frequency tables represents a data set. Which data set has the greatest mean?

Value	Frequency
$70$	$4$
$80$	$5$
$90$	$6$
$100$	$7$

Value	Frequency
$70$	$6$
$80$	$6$
$90$	$6$
$100$	$6$

Value	Frequency
$70$	$7$
$80$	$6$
$90$	$6$
$100$	$7$

Value	Frequency
$70$	$8$
$80$	$5$
$90$	$5$
$100$	$8$

ExplanationShow

Choice A is correct. The tables in choices B, C, and D each represent a data set where the values $80$ and $90$ have the same frequency and the values $70$ and $100$ have the same frequency. It follows that each of these data sets is symmetric around the value halfway between $80$ and $90$ , or $85$ . When a data set is symmetric around a value, that value is the mean of the data set. Therefore, the data sets represented by the tables in choices B, C, and D each have a mean of $85$ . The table in choice A represents a data set where the value $90$ has a greater frequency than the value $80$ and the value $100$ has a greater frequency than the value $70$ . It follows that this data set has a mean greater than $85$ . Therefore, of the given choices, choice A represents the data set with the greatest mean.

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

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

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

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

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