title: How to calculate mean based on number of votes/scores/samples/etc?
body: <p>For simplicity say we have a sample set of possible scores {0, 1, 2}.  Is there a way to calculate a mean based on the number of scores without getting into hairy lookup tables etc for a 95% confidence interval calculation?</p>
  
  <p>dreeves posted a solution to this here: <a href="https://stackoverflow.com/questions/280457/how-can-i-calculate-a-fair-overall-game-score-based-on-a-variable-number-of-match/281407#281407">How can I calculate a fair overall game score based on a variable number of matches?</a> </p>
  
  <p>Now say we have 2 scenarios ...</p>
  
  <p>Scenario A) 2 votes of value 2 result in SE=0 resulting in the mean to be 2</p>
  
  <p>Scenario B) 10000 votes of value 2 result in SE=0 resulting in the mean to be 2</p>
  
  <p>I wanted Scenario A to be some value less than 2 because of the low number of votes, but it doesn't seem like this solution handles that (dreeve's equations hold when you don't have all values in your set equal to each other).  Am I missing something or is there another algorithm I can use to calculate a better score.</p>
  
  <p>The data available to me is:</p>
  
  <ul>
  <li>n (number of votes)</li>
  <li>sum (sum of votes)</li>
  <li>{set of votes} (all vote values)</li>
  </ul>
  
  <p>Thanks!</p>