How to deal with the categorical variables with few data for prediction The image below shows how the rating for the heating quality will affect sale price.The data is about apartments and it's properties. E.g Rooms, GarageSize, BasementSize, etc. This visualization will be used to find the attributes to predict sales price of houses.
First question: How do we deal with "Poor" rating in this case? Do we remove category or do we proceed?
Second Question: What if the data we are trying to predict has a rating of "Very excellent" which do not belong in the testing data?
Note: I have not built a model yet

 A: My first question is why do you think you need to do anything special for the Poor heating group?  Simply because the group has less spread in housing doesn't mean that somehow data for it is less meaningful -- in fact, it may be just the opposite.  It's difficult to tell, however, if you have little spread for the Poor group because there is indeed little variability or if it's because you simply haven't collected much data that includes houses with Poor Heating.  If you discover that there is just too few data points in the Poor group, one thing that might be feasible to do is to collect additional data points.  In fact, it might even be recommended to "oversample" Poor heating homes so you can obtain sufficient data to make reliable predictions.  If you remove the Poor category and subsequently build a predictive model based on heating QC, you'll be unable to predict sales prices for homes that are rated poor (at least based on the Heating QC).
You should be very cautious extrapolating your predictions beyond your range of available data.  Since you do not currently have any data collected on Very Excellent Heating QC, you can't really make meaningful predictions about future Very Excellent Heating homes without some strong assumptions.  While it may appear that as one moves from Poor to Excellent the average price continues to increase, there is no data to suggest that this trend in fact continues on forever, or even at one higher rating, so caution should be exercised when trying to predict outside of the current set of values for which you have collected data.
