No wiki fcking answer to this
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.
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)].
The result is a negative number in this case.
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 plain arithmetic mean is actually a special case of the weighted mean, except all the weights are equal to 1. The arithmetic mean is the sum of all the individual observations divided by the number of observations. With a weighted mean you multiply each observation by a weight, add those values together and then divide by the sum of the weights. E.g. Let's say you have 3 observations: 4, 7, 12 The arithmetic mean is (4+7+12) / 3 = 23/3 = 7.67 Now let's assume that you want to weight the first observation by a factor of 10, the second observation by a factor of 5 and the third observation by a factor of 2: The weighted mean is (4x10+7x5+12x3) / (10+5+2) = 111/17 = 6.53 You can see that if all the weights were 1 you would have the arithmetic mean shown above. As it is mentioned above arithmetic mean is a special case of weighted mean. In the calculation of arithmetic mean all the observations are given an equal chance of occurance ie the above mentioned problem can be written as 4*1/3+7*1/3+12*1/3=7.67 or inother words 7.67 is the number it takes if all are given equal chance whereas in weighted mean the chance of occurance are not equal .This can be written as 4*10/17+7*5/17+12*2/17=6.53 in the above eg. 4 has given more weightage than 7 and 12 has the least weightage so the probability of 4 occurring is more when compared to 7 and 12 there fore the average obtained is seen to decrease as we have given more importance to 4 than others. It shows that the average is affected by the weightage given to the numbers