In reply to Martin not maisie:
Nope; Median is the middle value if you put all the answers in order in a row - it's the 50th centile - i.e. half the answers (not half the values) above & half below.
If any value has >50% of the answers then it must also be the median - I was probably able to prove that about 35 years ago.
Mode - correct.
Actually I can still prove it by a bit of logical deduction - 3 possibilities:
Assume the value with >50% of the answers is x.
1. Median is below x, therefore >50% must be below x, say 50+y %. Therefore total must be 50 + 50+y > 100% - ERROR.
2. Median is above x, therefore >50% must be above x, say 50+y %. Therefore total must be 50 + 50+y > 100% - ERROR.
3. Median is x - only possible remaining answer.
There is a type of case that might fail this - e.g. population is 0,0,1,1,2,2,2,2 - not sure what the median is then as it's between 1 & 2 and 2 has 50% of the answers.
Post edited at 12:54