Final answer:
The smallest the average of ten distinct positive integers could be when the median is 10 is 6.8.
Step-by-step explanation:
The smallest the average of ten distinct positive integers could be when the median is 10 is 6.8.
To find the average, we need to sum up all the integers and divide by 10. Since we have 14 integers, we can take the 6th and 7th values, which are 6.8 and 7.2, and average them to get 6.8.
Therefore, the smallest the average could be is 6.8.