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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.

Value	Data set A frequency	Data set B frequency
$30$	$2$	$9$
$34$	$4$	$7$
$38$	$5$	$5$
$42$	$7$	$4$
$46$	$9$	$2$

Data set A and data set B each consist of $27$ values. The table shows the frequencies of the values for each data set. Which of the following statements best compares the means of the two data sets?

ExplanationShow

Choice A is correct. The mean value of a data set is the sum of the values of the data set divided by the number of values in the data set. When a data set is represented in a frequency table, the sum of the values in the data set is the sum of the products of each value and its frequency. For data set A, the sum of products of each value and its frequency is $30 (2) + 34 (4) + 38 (5) + 42 (7) + 46 (9)$ , or $1, 094$ . It's given that there are $27$ values in data set A. Therefore, the mean of data set A is $\frac{1 , 094}{27}$ , or approximately $40.52$ . Similarly, the mean of data B is $\frac{958}{27}$ , or approximately $35.48$ . Therefore, the mean of data set A is greater than the mean of data set B.

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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