# Can median have decimal value for finding missing number?

I was wondering if it was possible to get the median as decimal value for finding the missing median? If there is an even number of numbers in the set, the median is the average of the two middle numbers, and the only way to find the missing number is if the median is one of those two numbers.

For example,
3 2 0 8 9 9 1 e
If the median is 4.5, which number could e be?


Would it possible to get median as a decimal value?

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Here we have $8$ numbers, so the median must have been computed by taking the average of the two "middle" numbers.

In our list we have $0$, $1$, $2$, and $3$. Since the median is $>3$, $3$ must be one of the "middle" numbers. The other middle number can't be $8$, for that would make the median larger than $4.5$. So the other middle number must be $e$, and we must have $$\frac{3+e}{2}=4.5.$$ Multiply both sides by $2$. We get $3+e=9$, so $e=6$.

Comment: This one was fairly straightforward. One can produce problems that have a similar look and feel but that are harder to figure out.

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+1, though strictly speaking the median of the numbers $3,2,0,8,9,9,1,6$ can be anything from $3$ to $6$, and you have to assume the convention of taking the midpoint of this range. – Henry Jul 6 '11 at 7:23
Is it legal to have the median value in decimals? – diya Jul 6 '11 at 7:37
@amala: Absolutely, fractions, decimals are all fine. – André Nicolas Jul 6 '11 at 8:02
@Henry: In the question, the OP referred very clearly to the midpoint convention, so it is reasonable to assume that this is the convention being used in his/her course. – André Nicolas Jul 6 '11 at 8:06
thanks for your kind help. – diya Jul 6 '11 at 8:19