| Value | Frequency |
|---|---|
| 1 | $a$ |
| 2 | 2$a$ |
| 3 | 3$a$ |
| 4 | 2$a$ |
| 5 | $a$ |
The frequency distribution above summarizes a set of data, where $a$ is a positive integer. How much greater is the mean of the set of data than the median?
Difficulty: Hard
| Value | Frequency |
|---|---|
| 1 | $a$ |
| 2 | 2$a$ |
| 3 | 3$a$ |
| 4 | 2$a$ |
| 5 | $a$ |