SOLUTION: Paul scores the following on math quizzes points each: 14, 6, 10, 16, 14. What can he score on test six and seven so that his range increases but the mean and median stays the same

Question 1031396: Paul scores the following on math quizzes points each: 14, 6, 10, 16, 14. What can he score on test six and seven so that his range increases but the mean and median stays the same?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
14, 6, 10, 16, 14 have mean 12 and median 14. The range is 10. (Verify all these!)
Let x and y be the last two quiz scores.
==> we want , or x+y = 24.
Also, since we want the range to increase, we must have y - minimum > 10.
The possible combinations are
x = 7, y = 17;
x = 6, y = 18;
x = 5, y = 19;
x = 4, y = 20;
x = 3, y = 21;
x = 2, y = 22;
x = 1, y = 23;
x = 0, y = 24;
You can check that all these are viable scores for the last two quizzes, since with these, the mean would still be 12, the median would still be 14, and the range would be greater than 10.
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