SOLUTION: The median of seven test scores is 82, the mode is 87, the lowest score is 70, and the average is 80. If the scores are integers, what is the greatest possible test score?

Put blanks for the seven test scores in order from smallest to largest:

__, __, __, __, __, __, __

Since the median is 82, we must put that in the middle:

__, __, __, 82, __, __, __

Since the lowest score is 70, we put that on the far left:

70, __, __, 82, __, __, __

Since the mode is 87, we either have

70, __, __, 82, 87, 87, __

or

70, __, __, 82, __, 87, 87

We are trying to get the greatest possible test score, so
if possible we would want it to be greater than 87, so we
try for the missing value to be greater than 87, so we
try this:

70, __, __, 82, 87, 87, __

The greatest score will be when the two smaller unknown scores
ones are as small as possible.  None of them can be the same
for then 87 wouldn't be the only mode.  So we make them as
small as possible, which are 71 and 72.

70, 71, 72, 82, 87, 87, x

where x represents the greatest possible value.

Since the average is 80,





469 + x = 560

      x = 91

So the largest possible score is 91

Edwin