How can I filter out anomalies / noise from a series of numbers? I'm looking to identify the minimum integer in a series.  However, occasionally there are integers that throw off this simple plan.  How can I ignore integers that are well outside the rest?
Example:
Day    Min    Max    Actual
  1      0    100      1-100
  2    101    200    101-104,106-200
  3    201    300    201-280,300
  4    105    400    105,305-400
  5    301    600    301-304,401-600

I need min/max output to be:
Day    Min    Max     Actual
  1      0    100      1-100
  2    101    200    101-104,106-200
  3    201    280    201-280,300       // filtered out 300
  4    305    400    105,305-400       // filtered out 105
  5    401    600    301-304,401-600   // filtered out 301-303

Can you suggest a strategy to ignore such anomalies?
Given a series like 301-304,401-600, I need to return 401-600.
 A: One idea is to find the average distance between consecutive integers, and filter away integers when the distance is too many times that average distance.  This does end up making the final list depend on how you filtered out the outliers.  In python:
maxJumpScale = 5
repeat = True
while ( repeat ):
    repeat = False
    average = sum(numbers)/numbers.size()
    averageDistance = max(1,(max(numbers)-min(numbers))/numbers.size())
    for i in range(1,numbers.size()):
        if ( numbers[i] > numbers[i-1]+maxJumpScale*averageDistance ):
            if ( numbers[i] < average ):
                numbers = numbers[i+1:]
                repeat = True
            if ( numbers[i-1] > average ):
                numbers = numbers[:i-1]
                repeat = True

A: Any filtering problem is essentially working from models of "ordinary" and "exceptional" values. There may be more than one category of "ordinary", likewise more than one category of "exceptional". Furthermore, you must also state your preferences as to whether it's worse to mistake ordinary for exceptional and vice versa. Once you have your models in hand, you compute the probability that any given datum falls into the various categories, and then calculate which assignment (i.e. putting the datum in which category) is most preferable. 
There are various heuristics for filtering and I'm sure you can make some up yourself. My advice is to try to do it from first principals.
You haven't said much about the problem domain so I can't really be specific about what you should do. Feel free to add more detail to the problem statement.
