This is a good open-ended problem that creates quality mathematical discussion. The median and the mean of the scores for Jenna and Kim are the same, which can require students to think of other possible solutions. A benefit of this task is that there is no one specific "correct" solution. There is also no prescribed method for solving the problem. Incorporating these types of problems leads to increased engagement and discussion in class. 

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There were five judges for a figure skating competition: The top two competitors were Jenna and Kim. They received the scores below.
 
Jenna     8           6         10        9          7
Kim          9          9          7          8         7
 
Who should win?

A teacher stood before a class of thirty senior mathematics students. Before he passed out the final exam he stated, “I have been privileged to be your instructor this semester, and I know how hard you have worked to prepare for this test. Because I am confident that you know this material, I am prepared to offer an automatic B to anyone who opts to skip taking the final exam.”

There was great relief for some. A number of students went right for the offer and thanked the teacher.

“Last chance,” said the teacher and one more student went.

The instructor then handed out the final exam, which consisted of two sentences. “Congratulations,” it read, “you have just received an A in this class. Keep believing in yourself."