Jeanette received an integer grade between 1 and 10 inclusive, for each of her lab reports. She said that the arithmetic mean, median, and mode of all her lab grades were 8, 7, and 8 respectively.

Is this possible? If so, find a grade distribution consistent with the data; if not, prove it.

(In reply to solution by Charlie)

I believe that to "assume ... an even number of grades with the same number below 7 as above" adds constraints to the problem.

In your posting, before the 10's are added, your mean is "clearly below 7". Since the addition (in paragraph 3 of your posting) of 10's and 5's must have a mean of at most 7.5, this implies a total combined mean of less than 7.5. But, for example, the distribution: two 5's, ten 6's, ten 7's, eleven 8's, and ten 10's has a mean of greater than 7.6 

Posted by Dennis on 2007-05-24 12:17:02