# Help deriving an equation.

• March 1st 2012, 07:40 AM
datanewb
Help deriving an equation.
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:

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

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

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

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.
• March 1st 2012, 07:47 AM
emakarov
Re: Help deriving an equation.
Let's denote oldMean by m, newMean by m' and newVal by v. Then

$m'=\frac{mn+v}{n+1}=\frac{mn+m-m+v}{n+1}=\frac{m(n+1)+v-m}{n+1}=m+\frac{v-m}{n+1}$