The median is the score in the middle of the list of scores so that 50 percent of the scores fall above it and 50 percent fall below it. In a list of 15 scores, it is the eighth score. The median is not sensitive to extreme scores. It may or may not be the same value as the mean for a group of data. The mode is simply the score which appears the most often in your group of data.
Some groups have more than one mode, of course.
The standard deviation is a measurement of the spread, or dispersion, of a distribution of scores. On the other hand, non-parametric tests make fewer assumptions about the data distribution. If you cannot make the assumptions, then non-parametric tests may be more appropriate. These tests do not require normal distributions or equal group variance. These tests are based on ordinal or even nominal measurement and are highly useful for quick calculations.