Item — sat-dog

? Math · None · None · MCQ Q23

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?

A
The mean of the new data set is greater than the mean of the original data set, and the median of the new data set is greater than the median of the original data set.
B
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.
C
The mean of the new data set is less than the mean of the original data set, and the median of the new data set is less than the median of the original data set.
D
The mean of the new data set is less than the mean of the original data set, and the medians of the two data sets are equal.

Correct answer: B (parsed from the explanation — this source omits an answer key for this item)

Explanation

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 71 39 weights of the tortoises in the original data set and one additional weight, . 39 Since the additional weight, , 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 71 of tortoises and is in ascending order, the median of the original data set is 36 represented by the middle value, or the th value. Based on the frequencies 36 17 shown in the table, the th value in this data set is . 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 72 set consists of the weights of tortoises, the median of the new data set is 36 37 between the th and th data values when the values are arranged in 39 ascending order. To keep the data in ascending order, the additional value of would be placed at the bottom of the frequency table with a frequency of 1. 36 37 Therefore, based on the frequencies in the table, the th and th values in the 17 17 new data set are both . It follows that the median of the new data set is , 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.

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