Final answer:
The correct answer is option a. An even-numbered data set has a single median, which is calculated as the average of the two middle numbers when the data are arranged in ascending order.
Step-by-step explanation:
When working with a data set where the number of data values n is even, the calculation of the median does not result in a single middle value, because there is not one middle number but two. Instead, we determine the median by taking the average of these two middle numbers. For example, if we have a data set with 14 numbers, after arranging the data in ascending order, the median would be the average of the 7th and 8th values. Let's say those values were 6.8 and 7.2. To find the median, you would add them together, getting a sum of 14, and then divide by 2, resulting in a median of 7.
Applying this approach to any even-numbered data set will provide the correct median value. Therefore, the correct answer to the question of whether an even-numbered data set has one median, two medians, or no median is: a) one median because it is the average of the two centermost numbers.