Just because a value is far away from the mean does not necessarily mean that this is a bad/wrong value.

There is never a good statistical reason to exclude a value as being "outlying". In small samples, it may happen that a value is a bit "off" from the rest. Here it could easily be that this value provides very relevant information, correcting some (possible) bias in the estimates of the mean and variance. In large samples, outliers are rare. And if they exists, they don't have any relevant impact on the results, so they can be ignored.

However, there are good practical reasons to exclude values that are very highly implausible or even impossible (physically, biologically; so that values must be the result of some error). It would be wrong to include values in an analysis that are obviously wrong. It is generally simple to identify impossible values (e.g. a negative weight, or a blood pressure that would disrupt the organs), and with some expert knowledge it is also possible to identity highly implausible values. But sometimes we don't have enough knowledge to judge what is an implausible or even impossible value (if someone tells me that a fluorescence values indicating a protein expression in a cell is 534.2 AU, then I have no clue if this is reasonable, typical, strange or impossible. I can't say anything. So I must believe that if the experiment is conducted with great care and all necessary controls are done and ok, that this value is ok, too).

Looking at the distribution of the data to identify "outliers" (values that - for whatever reason! - are substantially far away from the rest) helps to spot possible problems. One can then go back and check the lab book and other notes that indicate a possible and plausible source of an error. If this is identified, then the value should be excluded. Otherwise, the value should be retained. Note that it is not really relevant to give some "cut-off", like Median ± 3xIQR or something like this. Plot the data and just have a look. If there are possibly problematic values, then you will see them.

Finally, be aware that distributions don't need to be symmetric. They can be skewed - and this will make (relatively many) values look like being outliers. In biology, many (actually most) variables are skewed, more log-normal or gamma-distributed than normal-distributed (e.g. concentrations, intensities, pressures). you will find "outliers" preferably towards too large values. Looking at appropriately (typically log-) transformed values, all "outliers" suddenly disappear (usually).

https://ih1.redbubble.net/image.1431746256.7821/pp,840x830-pad,1000x1000,f8f8f8.jpg