urgent help weighted mean

Question

1. How to know when to use weighted mean in a question? And could someone explain the formula, and what it means please! Thank you so much.

Answer 1

Hi Gary,

The weighted mean can be used when you are trying to summarize a set of values but apply different "weights" or "importance" to each value. If a value in the set has a higher weight, it can be said to be more important and will affect the final summarized value more greatly than the other values in the set.

As for when to use it, I think it would depend on the question.

For example, I am trying to buy a car and I have 3 criteria that I rate from 1-5.

1. Comfort
2. Price
3. Spaciousness

If I really cared about Comfort but not Spaciousness, I could give the Comfort category a higher weight than the Spaciousness category. Lets assign the weights for each category as shown below:

Comfort = 10, Price = 5, Spaciousness = 0. Note that Spaciousness has 0 weight, which would that the value for the Spaciousness category would not impact or affect the weighted average value in the end at all.

If I was comparing 2 cars with the following values, we can see how the weighting affects the final summarized value.

Car A: a less comfortable car but with a lot of space

1. Comfort Value = 2
2. Price = 3
3. Spaciousness = 5

Car B: a more comfortable car with no space (maybe it's only got 1 seat :) )

1. Comfort Value = 5
2. Price = 3
3. Spaciousness = 0

The equation for Weighted Average is:

(Sum of (Category Value * Category Weight)) / (Sum of Category Weights)

Car A would score:

(2 * 10 + 3 * 5 + 5 * 0) / (10 + 5 + 0) = (20 + 15) / 15 = 2.333

Car B would score:

(5 * 10 + 3 * 5 + 0 * 0) / (10 + 5 + 0) = (50 + 15) / 15 = 4.333

Based on the weightings I chose, Car B would have a higher weighted average than Car A.

An interesting thing to note is that the Spaciousness category did not affect the final weighted average for either of the cars. That is because in my initial weighting, I had given the Spaciousness category a weighting of 0, indicating that I don't care about that score at all. Inversely, the comfort category greatly affected the final weighted average.

Looking at the Weighted Average equation, we can also learn a few interesting things. Let me use the example above. The equation for the example above is as follows:

(Comfort Value * Comfort Weight + Price Value * Price Weight + Spaciousness Value * Spaciousness Weight) / (Total Weights)

... where Total Weights = Comfort Weight + Price Weight + Spaciousness Weight ...

Comfort Value * Comfort Weight/Total Weight + Price Value * Price Weight/TotalWeight + Spaciousness Value * SpaciousnessWeight/Total Weight.

By splitting the equation this way, I think it helps explain the equation alittle better. What we see multiplied to each of the values is "some weight"/Total Weight. This value would describe the percentage of the final value that is from this specific category.

Take the spaciousness example:

Spaciousness Weight / Total Weight = 0 / 15 = 0%. This would indicate that the Spaciousness Value accounts for 0% of the final weighted average which is another way to say that it would not affect the final weighted average at all.

Hope that helps!

- Aaron

Answer 2

Best REAL WORLD example of a "weighted mean" is YOUR GPA!

Let's say you are taking 6 classes this year:

Math ----- this class is worth 3 credits ---- You get a C in math class

English ----- this class is worth 3 credits ---- You get a B in English

History ----- this class is worth 3 credits ---- an A in History

Science ----- this class is worth 3 credits --- a C in Science

Cooking ----- this class is worth 1 credit --- an A in Cooking

Art History ----- this class is worth 2 credits --- an B in Art History

Here are your weight factors for each letter grade: A = 4; B = 3; C = 2; D = 1; F = 0

So, now you take the number of credits each class is worth and multiply it by the weight factor of the grade you received for each class. Math - 3 credits x 2 grade points (C) = 6 grade pts

English - 3 credits x 3 grade points (B) = 9 grade pts

History - 3 credits x 4 grade points (A) = 12 grade pts

Science - 3 credits x 2 grade points (C) = 6 grade pts

Cooking - 1 Credit x 4 grade points (A) = 4 grade pts

Art History - 2 credits x 3 grade points (B) = 6 grade pts

Now, just like in calculating a REGULAR MEAN (AVERAGE), you will add all of those grade points up to find the sum/total grade points. (6 + 9 + 12 + 6 + 4 + 6 = 43 points and divide that by the number of credits earned - which is (3 + 3 + 3 + 3 + 1 + 2 = 15).

43/15 = approximately 2.87 GPA (grade point average). Weighted average help to place more importance or significance on certain scores or numbers. The better the grades the higher the average.

Answer 3

You take 5 tests, each worth 10 points. then you take a final exam worth 50 points

You get 80 on each test and a 100 on the final exam.

Your final grade is a weighted average of 90

80 x 1/10 + 80 x 1/10 + 80 x 1/10 + 80 x 1/10 + 80 x 1/10 + 100 x 1/2

8 + 8 + 8 + 8 + 8 + 50 = 90

each grade is weighted by a fraction that indicates its importance.

each test was worth 1/10 of the grade. final worth 1/2 the final grade

or 80(10) + 80(10) + 80(10 + 80(10 + 80(10 + 100(50 = 4000+5000=9000 points. Divide by total points

9000/100 = 90= weighted average score