Weight (pounds) Frequency 13 12 14 8 15 5 16 7 17 9 18 10 19 13 20 7 The

Question

Weight (pounds) Frequency 13 12 14 8 15 5 16 7 17 9 18 10 19 13 20 7 The frequency table summarizes a data set of the weights, rounded to the nearest pound, of 71 tortoises. A weight of 39 pounds is added to the original data set, creating a new data set of the weights, rounded to the nearest pound, of 72 tortoises. Which statement best compares the mean and median of the new data set to the mean and median of the original data set?

Accepted Answer

Choice B is correct. The mean of a data set is the sum of the values in the data set divided by the number of values in the data set. The new data set consists of the weights of the 71 tortoises in the original data set and one additional weight, 39 . Since the additional weight, 39 , is greater than any of the values in the original data set, the mean of the new data set is greater than the mean of the original data set. If a data set contains an odd number of data values, the median is represented by the middle data value in the list when the data values are listed in ascending or descending order. Since the original data set consists of the weights of 71 tortoises and is in ascending order, the median of the original data set is represented by the middle value, or the 36 th value. Based on the frequencies shown in the table, the 36 th value in this data set is 17 . If a data set contains an even number of data values, the median is between the two middle data values when the values are listed in ascending or descending order. Since the new data set consists of the weights of 72 tortoises, the median of the new data set is between the 36 th and 37 th data values when the values are arranged in ascending order. To keep the data in ascending order, the additional value of 39 would be placed at the bottom of the frequency table with a frequency of 1 . Therefore, based on the frequencies in the table, the 36 th and 37 th values in the new data set are both 17 . It follows that the median of the new data set is 17 , which is the same as the median of the original data set. Therefore, the mean of the new data set is greater than the mean of the original data set, and the medians of the two data sets are equal. Choice A 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.

Weight (pounds)	Frequency
$13$	$12$
$14$	$8$
$15$	$5$
$16$	$7$
$17$	$9$
$18$	$10$
$19$	$13$
$20$	$7$

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