Question 175749: The mean of a 13 item data set is 320. 11 of the items are 300, 320,199,175,325,520,156,225,326,421 and 504. The median is 325. Find the remaining two items in the set if it is known that these two items have the greatest possible difference.
Please explain in easy words and complete detail !!!!!!!!!!!!
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441)   (Show Source):
Answer by Edwin McCravy(20065)  (Show Source):
You can put this solution on YOUR website! Warning! Josmiceli's solution is incorrect.
He thought the smaller missing
number had to be at least 1 larger
than the median, but it can be equal
to the median. Here's the correct
solution by Edwin:
Let the two missing number be x and y, where x is the
smaller of the two missing numbers and y is larger of the
two missing numbers.
Now we arrange the 11 given numbers from smallest to largest:
156, 175, 199, 225, 300, 320, 325, 326, 421, 504, 520
Since there are 13 numbers, an odd number of numbers, the
7th one must be the median because: Of the other 12 numbers,
half of them, 6, are below 325 and the other 6 are above 325.
Since 325 is already the 7th one from the bottom in the
list, the smaller one, x, must be either equal to 325
or larger. but the difference will be the greatest
when the smaller, x, is exactly 325. So, substituting
325 for x is
So the smaller missing number is 325, and
the larger missing number is 364.
Edwin
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