How do outliers effect data? In particular I'm curious about how they effect mean, median, and mode. Are outliner data able to be dismissed or not?

The outlier affects the mean by pulling the mean towards it.  For instance, in a set of data like:  1, 2, 3, 4, 2 the mean is 2.4. However if you add 12 to the set of data, which is significantly higher, the mean is now 4, pulling it closer to 12.  The median, also known as a middle score, and the mode is largely unaffected by an outlier. The outlier can also have a larger impact on the range of a set of data.  Before you dismiss the data you must analyze the meaning of the outlier and what is is you are calculating and why.