Question 1203772: 10. If the average of 5 positive integers is 70, what is the largest possible
value of their median?
(A) 70
(B) 114
(C) 116
(D) 346
Found 2 solutions by math_helper, greenestamps:
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website!
Assume the sorted dataset is {d1,d2,d3,d4,d5}
The given information about the mean indicates the SUM d1+d2+d3+d4+d5 is 5*70 or 350.
The median is the middle number (or average of the two numbers on either side of the "middle" for datasets with an even number of elements). The data elements must first be sorted (e.g. lowest to highest) when finding the median.
For the problem at hand, clearly, you can not have a median of 346 because then  and even setting d1=d2=1 (the minimum possible values) would result in a sum of 1040. (1040/5 = 208, and 208 > 70).
What about 116? Would that work?
For a potential median of 116, if d3=d4=d5=116, you have { d1, d2, 116, 116,116}
and since 3*116 = 348, you can set d1=d2=1 and get the desired sum. So the maximum median is 116. In this case, the dataset would be {1,1,116,116,116}
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
The sum of the 5 numbers in the set is 5*70 = 350.
To have the largest possible value for the median, you need to have
(1) the two smallest numbers as small as possible; and
(2) the three largest numbers (i.e., including the median) as close together as possible.
The numbers are all positive integers, so we want the smallest two numbers to both be 1.
That means the sum of the largest three numbers is 350-2 = 348.
Three integers as close together as possible with a sum of 348 means each of the numbers must be 348/3 = 116.
The five numbers are 1, 1, 116, 116, and 116.
ANSWER: (C) 116
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