To determine the best measure of center for the given data set, we need to consider the values and their distribution.
The data set is as follows: 108, 96, 96, 84, 108, 240, and 84.
The median represents the middle value when the data set is arranged in ascending or descending order. In this case, when we arrange the data in ascending order, we have: 84, 84, 96, 96, 108, 108, 240. The middle value is 96, which is the fourth value in the sorted data set.
The mean is calculated by summing up all the values and dividing by the total number of values. In this case, the sum of the values is 756 (108 + 96 + 96 + 84 + 108 + 240 + 84), and there are seven values. Therefore, the mean is 756/7 = 108.
Comparing the options:
A: median because all of the values are close to one another in value - This is not accurate as the values vary, and the median is not necessarily the best measure of center based on the values being close to one another.
B: mean because all of the values are close to one another in value - This is not accurate as the values are not all close to one another, and the mean is not necessarily the best measure of center based on the values being close to one another.
C: median because 240 is much higher than the other numbers in the data set - This is not accurate as the presence of a single high value does not automatically make the median the best measure of center.
D: mean because 240 is much higher than the other numbers in the data set - This is the most accurate option. The mean takes into account the magnitude of each value and is influenced by extreme values. The value 240 has a significant impact on the mean, making it a better measure of center in this case.
Therefore, the best measure of center for this data set is D: mean because 240 is much higher than the other numbers in the data set.