Does it make sense? In my data set of 10 exam scores, the mean turned out to be the score of the person with the third highest grade. No two people got the same score.

Yes

Step-by-step explanation:

Given that In my data set of 10 exam scores, the mean turned out to be the score of the person with the third highest grade.

No two people got the same score.

Let the scores be a, b, c, d, e in ascending order where no two scores are equal

If a+b=d+e = 2c then we can have c as the mean of the scores of 5 persons

This is because

Total sum = a+b+c+d+e = (a+b) + c + (d+e)

= 2c+c+2c=5c

Average = 5c/5 = c

It makes sense and there are chances as long as the above condition is satisfied.