How do I calculate a weighted average from two averages? I have two sets of averaged data I am working with, which account for a score and the average amount of users that achieved this.
For example:
Average Score $4$, 
Total Number of participants (which the average is derived from): $835$
Average Score $3.5$,
Total Number of participants: $4,579$
Can I calculate a weighted mean from these two averages and participant counts, or would that be inaccurate? 

Assume that group 1 has an average of $m_1$ and size $N_1$ and group 2 has an average of $m_2$ and size $N_2$ then you can take the weighted average of the two means two get the overall mean:
$$
m= m1\cdot \frac{N_1}{N_1+N_2}+m2\cdot \frac{N_2}{N_1+N_2}.
$$
