Mean, Median, and Mode

Mode:
--------
The mode is the value that appears most often in a set of data.

The mode of a discrete probability distribution is the value x at which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled. Not the value itself. As for a discrete set of numbers 1, 2, 3, 3, 3, 2, 1 the mode is the value 3.

The mode of a continuous probability distribution is the value x at which its probability density function has its maximum value, so, informally speaking, the mode is at the peak.
 

As noted above, the mode is not necessarily unique, since the probability mass function or probability density function may take the same maximum value at several points x₁, x₂, etc.

Mean:
--------