Question

re of central tendency. part 6 of 6 points: 0.83 of 1 the number of credits being taken by a sample of 13 full - time college students are listed below. find the mean, median, and mode of the data, if possible. if any measure cannot be found or does not represent the center of the data, explain why 7 9 10 10 7 6 6 6 8 6 6 6 7 a. the median represents the center. b. the median does not represent the center because it is the smallest data value. c. the median does not represent the center because it is the largest data value. d. the median does not represent the center because it is not a data value. e. the data set does not have a median find the mode. select the correct choice below and, if necessary, fill in the answer box to complete your choice a. the mode(s) is/are 6 (type an integer or decimal rounded to one decimal place as needed. use a comma to separate answers as needed.) the data set does not have a mode. does (do) the mode(s) represent the center of the data? a. the mode(s) represent(s) the center b. the mode(s) does (do) not represent the center because it (one) is the smallest data value c. the data set does not have a mode d. the mode(s) does (do) not represent the center because it (one) is the largest data value e. the mode(s) does (do) not represent the center because it (they) is (are) not a data value

Explanation:

For the question "Does (Do) the mode(s) represent the center of the data?"

The mode is 6. Let's check the data set: 6, 6, 6, 6, 6, 7, 7, 7, 8, 9, 10, 10 (after sorting). The mode (6) is the smallest value in the data set? Wait, no, when we sort the data: 6, 6, 6, 6, 6, 7, 7, 7, 8, 9, 10, 10? Wait, wait, the original data is 7, 9, 10, 10, 7, 6, 6, 6, 8, 6, 6, 6, 7. Let's count the number of elements: 13. So sorting them: 6, 6, 6, 6, 6, 7, 7, 7, 8, 9, 10, 10? Wait, no, let's list all 13:

Original data: 7, 9, 10, 10, 7, 6, 6, 6, 8, 6, 6, 6, 7. Let's count the 6s: let's see, 6 appears at positions 6,7,8,10,11,12? Wait, no, let's list each number:

1:7, 2:9, 3:10, 4:10, 5:7, 6:6, 7:6, 8:6, 9:8, 10:6, 11:6, 12:6, 13:7. Wait, no, that's 13 numbers. Let's sort them in ascending order:

6, 6, 6, 6, 6, 6, 7, 7, 7, 8, 9, 10, 10. Wait, now I see: 6 appears 6 times (positions 1 - 6), then 7 appears 3 times (7 - 9), 8 once (10), 9 once (11), 10 twice (12 - 13). So the mode is 6, which is the smallest value in the data set? Wait, no, 6 is the smallest value here (since the data starts at 6). Wait, but the mode is the most frequent value. Now, does the mode represent the center? Let's think about the center. The median is the middle value (7th value when sorted: 7). The mean: let's calculate. Sum of data: 66 + 73 + 8 + 9 + 10*2 = 36 + 21 + 8 + 9 + 20 = 94. Mean is 94/13 ≈7.23. The mode is 6, which is the smallest value. So the mode (6) is the smallest data value, so it doesn't represent the center. So the correct option is B: "The mode(s) does (do) not represent the center because it (one) is the smallest data value."

Answer:

B. The mode(s) does (do) not represent the center because it (one) is the smallest data value.