# Probability of mode value in a given series [closed]

I’m developing software which needs some math which is outside of my wheelhouse.

I have a series of numbers, each single number in the series is submitted by a user. I want to determine the probability that the mode number in the series is the correct number. We’ll assume that we have no prior knowledge and so any number could be correct, but the most common number is most likely correct.

For instance, we have the series [3, 3, 5, 3], what are the odds (expressed as a %) that the true number is 3? (We must assume that the mode number is the "true number" otherwise this problem becomes impossible I believe.)

Bonus: if we assign a reputation to each user (expressed as the percentage of their submissions that are not the mode value for a given sequence), we can determine that some users are less “trustworthy” and we could factor that into the original confidence %.

## closed as unclear what you're asking by user158565, Michael Chernick, kjetil b halvorsen, mkt, Peter Flom♦Feb 6 at 10:55

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• We have to have some way of assessing what the correct number is. At least, tell us what numbers could be correct. Every real number? Every rational number? Integers only? Positive integers? Positive integers less than 10? or 20? With uniform probability of correctness? Each one of these decisions changes the likelihood that 3 or 5 is correct. – Peter Leopold Feb 6 at 5:54
• This continues to make no sense. You ask, "what are the odds (expressed as a %) that the true number is 3?" (where 3 is the modal value), & assert that, "We must assume that the mode number is the 'true number'". Therefore, the probability is $1$ (by definition), & the odds are undefined ($1/0$). As @PeterLeopold notes, you need some external information about the correct number, otherwise you have nothing. – gung Feb 6 at 14:20