I have a series of numbers: $1,2,3$
I'm calculating a simple average between, them $(2)$.
Now, I'm deleting the series and have no information regarding how many elements there were in the series or what the series item values are, but I keep the average value $(2)$.
Now, I have another series: $4,5,6$. I calculate the average $(5)$.
Is it correct to say that if I take the previous series average $(2)$ and do a new average between it and the new series average $(5)$, I will always get an accurate result for the average of the combination of the two series (series$$ and series$$)?