I came across the following problem:
A list of 11 positive integers has a mean of 10, a median of 9, and a unique mode of 8. What is the largest possible value of an integer in the list?
From the information, I got the following information:
- 11 integers with a mean of 10 means a total must be 110.
- A unique mode means that there must be at least two 8's.
- if there are two 8's, and the median is 9, there must be at least two numbers greater than 9 also.
However, I can't figure out exactly what to do from here. Any help would be appreciated!