Weighted Average

Question 1

Easiest example of a weighted average from my own life is…

Answer 1

Grading policies, different exam weights

Question 2

When estimating weighted averages, what type of average is useful and why?

Answer 2

When you have the equally weighted average, you know the fulcrum point between both values if they were weighted 50/50
In this scenario your answer must exclude that number, as it forms a number line range towards the value that has the dominant weight.

So if your weights are similar to 50/50 you can estimate approximates…

Question 3

If it’s an equally weighted average problem and there are 7 terms… what is the weight for the algebraic method?

Answer 3

1/7, always will be 1 / # of terms

Question 4

The Algebraic method from Dr. Piao’s class is ONLY useful when…

Answer 4

Dealing with easy numbers. Otherwise it is inefficient to calculate X1W1 + X2W2….

Question 5

What method helps visualize the relationship and simplify the process…

Answer 5

Teeter totter method. Build a simple scale. Whichever value has the dominant weight, draw diagram to express gravity pushing down on it. Then have the equally weighted number written into fulcrum

Question 6

How to find precise Weighted Average Value?

Answer 6

1. Find the range between the 2 values. Greatest - smallest
2. Multiply the weights of whichever value you’re curious about by the range… it’ll reveal how much of that distance a value is responsible for

Exp. If the dominant weight is 60%… multiply the range by that percent… then add to the submissive value. On the diagram this makes sense since the dominant value pushes the number beyond the halfway point

Question 7

What if the Q asks about finding the weights instead of the average?

Answer 7

Reverse engineer the process of finding the distance between the 2 values. Plot the weighted average on the scale. Then develop a fractional relationship to convert into a %

Question 8

Mixture Q’s combine…

Answer 8

averages, ratios and percentages typically

Question 9

If the question is asking what is the ratio between the Krispy ingredient to the Sugar Ingredient…

Answer 9

Rewrite as a fraction of K / S

Q basically asked what is K per S

Question 10

Solve: K is 10% sugar, B only has 2%. How would you make a mixture of 4%, what would the ratio of K to B end up as?

Answer 10

Make formula that shows:
Individual averages = Desired weighted average

.1 K + .02B = .04 (K +B)

1. Multiply to remove decimals
2. solve for K/B