Not to brag, but I can be used for both discrete and continuous numeric data. I also take account of all values unlike the other two guys.
Can someone tell me what is the average score of this test?
Don't worry! I will handle all of this!
I want to know what is the mean number of assignments that my collegue gets each week.
But I do admit that I am not always representative of the data, and may not reflect the centre of the distribution as well as the other two, because in some cases, especially for continuous data, I might not exist at all. The presence of more than one of me can limit the ability of me in showing the centre or typical value of the distribution because a single value to describe the centre cannot be identified.
The mean did not tell you that it can be easily affected by outliers and skewed distributions, and it cannot even be calculated for categorical data
The median is actually quite useless most of the time. It cannot be identified for categorical nominal data, as it cannot be logically ordered.