A data set contains 10 distinct positive integers. The mean (arithmetic average) of these 10 integers is 50. A new positive integer, , is added to the data set, creating a new data set of 11 integers. Which of the following statements must be true?
If , the mean of the new data set is greater than 50.
If , the mean of the new data set is less than 50.
If , the mean of the new data set is greater than 50.
The mean of the new data set is always greater than 50, regardless of the value of .
