title: General - Is there a way to calculate an average based off of an existing average and given new parameters for the resulting average?
body: <p>Lets say, we're calculating averages of test scores:</p>
  
  <p>Starting Test Scores:  75, 80, 92, 64, 83, 99, 79 </p>
  
  <p>Average = 572 / 7 = 81.714...</p>
  
  <p><strong>Now given 81.714, is there a way to add a new set of test scores to "extend" this average if you don't know the initial test scores?</strong></p>
  
  <p>New Test Scores:  66, 89, 71</p>
  
  <p>Average = 226 / 3 = 75.333...</p>
  
  <p>Normal Average would be:  798 / 10 = 79.8</p>
  
  <p>I've tried:</p>
  
  <pre><code>Avg = (OldAvg + sumOfNewScores) / (numOfNewScores + 1)
  
  (81.714 + 226) / (3 + 1) = 76.9285
  
  Avg = (OldAvg + NewAvg) / 2
  
  (81.714 + 79.8) / 2 = 80.77
  </code></pre>
  
  <p>And neither come up the exact average that it "should" be.  Is it mathematically possible to do this considering you don't know the initial values?</p>