Geometric mean
There is no specific collective noun for a group of graphs, in which case any noun that suits the context can be used; for example a pile of graphs, a display of graphs, a collection of graphs, etc.
The weighted mean is simply the arithmetic mean; however, certain value that occur several times are taken into account. See an example http://financial-dictionary.thefreedictionary.com/weighted+average
A "weight" in these circumstances is equal to the number of times an entry is used in calculatin the average. Suppose we find the average of 1, 2, and 6. It is (1+2+6)/3 = 3. But suppose the value for 2 is regarded twice as reliable or important as the others. In that case you put it into the calculation twice: (1+2x2 + 6)/4=3.75 and that is a weighted average with the second item having weight 2. In general, you add up all the terms all with their own weights applied (some may be 1, some less than 1, some more than 1) and then divide by the sum of the weights, to finish up with a weighted average.
Graph a few of them, and watch for trends! Anyway, I assume you are talking about polynomials; in the case you mention, the general tendency is for the graph to go from the top-left, towards the bottom-right.
The result is a negative number in this case.
A weighted average multiplies each data point by an arbitrary 'weight' and divides by the sum of the weights. Your everyday garden variety average, or arithmetic mean, is actually a special case of a weighted average, except all the weights are equal to 1. Selection of weights are largely arbitrary but generally based on sound reasoning (e.g. relative population sizes). As another example, let's say you have 5 reviewers of a product giving their overall satisfaction rating. The scores are 9, 7, 6, 7, 3. However you have a very high regard for Reviewer 1 so you assign her a weight of 15 (and the others remain at weight=1). The average score is (9+7+6+7+3)/5=6.4 The weighted average score is (15*9+7+6+7+3)/(15+4)=8.3 The weighted average is much closer to Review 1's opinion due to your weighting decision. The weight is often NOT arbitrary as in the above example. If a bank wants to know the average interest rate for its portfolio, the weight is the principal balance of each loan. If there are only two loans, one for $999,990 at 6% and one for $10 at 12%, the AVERAGE RATE is 9% [(6 + 12)/2]. However, the weighted average rate is only 6.00006% [(((.06*999990)+(.12*10))/1000000)].
No they shouldn't be in case you make a mistake or smudge it or go wrong.
The result in this case is positive.
The result is negative in this case.
Remember that when dividing two negative values, we obtain a positive result. The signs case for product is the same for this case.
The same as any two fractions. In this case, the answer will be negative.