SOLUTION: I keep trying to get help with this problem but nobody answers. HELP. On an algebra test taken by all but one student in a class, the mean score is 82 and the median score is 81.5.

Question 947142: I keep trying to get help with this problem but nobody answers. HELP. On an algebra test taken by all but one student in a class, the mean score is 82 and the median score is 81.5. All test scores were integers between 0 and 100 inclusive. The student who was absent takes the test later and scores 86. Find the absolute value of the difference between the mean and the least possible median for all of the 25 students in the class who took the test. Express your answer as an exact decimal. Thanks for your help.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
To calculate the new mean,

So then,

Since the median was 81.5, it's the average of the highest score in the lowest 12 and the lowest score in the highest 12. The lowest possible score in the highest 12 would have been 82. This score became the lowest possible median when the 86 was scored.
So then,

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