Mean and Median Calculations

Question

A group of 20 has a mean = 85 and median = 80. A different group of 30 has a mean = 75 and median = 72. Now, what is the mean of and median for the entire group of 50?

Answer 1

Hint: Use the idea of a weighted mean.

Answer 2

This is an elaboration on the answer from response, in case you didn't see weighted averaging before.

So you have $(x_i)_{i=1}^{20}, (y_i)_{i=1}^{30}$ with $\frac{1}{20} \sum_{i=1}^{20} x_i = 85$ and $\frac{1}{30} \sum_{i=1}^{30} y_i = 75$.

Thus, $\sum x_i = 20 \cdot 85$ and $\sum y_i = 30 \cdot 75$ hence total average is $$ \frac{\sum x_i + \sum y_i}{50} = \frac{20 \cdot 85 + 30 \cdot 75}{50} = 79. $$

EDIT Not sure what to do with the weighted median. To tell exactly, you would need the entire numer range, since it's the middle value. The only thing you can guarantee is that at least half the numbers will be $\geq 72$ and at least half the numbers will be $\leq 85$, so the median $m$ is guaranteed to satisfy $72 \leq m \leq 85$.