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Problem-Solving and Data Analysis Difficulty: Hard

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

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?

The mean of data set A is greater than the mean of data set B.

The mean of data set A is less than the mean of data set B.

The mean of data set A is equal to the mean of data set B.

There is not enough information to compare the means of the data sets.

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Explanation

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 $StartFraction 1,094 Over 27 EndFraction$ , or approximately $40.52$ . Similarly, the mean of data B is $StartFraction 958 Over 27 EndFraction$ , 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.