I believe that the following two equations are equivalent, but I am unable to algebraically derive one from the other. For computing a running average, I believe the following formula is correct where n = number of values in oldMean:

$\displaystyle newMean = ((oldMean * n) + newVal ) / (n + 1) $.

Similarly, I found this equation which I think does the same thing:

$\displaystyle newMean = oldMean + (newVal - oldMean) / (n + 1) $.

Are these equations in fact equivalent? They both seem to work when calculating a running average. If they are equivalent, how do I derive one from the other?

Thank you. This seems like an easy problem, but I've managed to confuse myself.