The mean of 5 different test scores is 10, what are the largest and smallest possible values fpr the median, all test scores are whole numbers

Question

Largest median in 5 different test scores. Smallest median in 5 different test scores. Mean of test scores are 10

Answer 1

If n is the size of an ordered dataset, then 10n is the sum of the data, and no individual data element can exceed 10n. If there exists one such element=10n, all other elements must be zero, assuming that zero is the lowest possible test score. This implies that median=0, the minimum median value, because the central element has to be zero.

Conversely, if all but one element is the greatest value g, then g will be the median. The remaining element x has to make up the total, so we need to solve (n-1)g+x=10n. Therefore, g=(10n-x)/(n-1). The maximum value of g is when x=0, so g=10n/(n-1). We’re told that g must be a whole number, so g=10+10/(n-1). When n=5, g=10+2.5, making g=12. The remaining element x=2. 

So, the minimum median is 0 and the maximum is 12.