Inactive Tutor answered • 05/31/21
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.
- Comfort
- Price
- 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
- Comfort Value = 2
- Price = 3
- Spaciousness = 5
Car B: a more comfortable car with no space (maybe it's only got 1 seat :) )
- Comfort Value = 5
- Price = 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
Gary H.
but could you explain the definition and formula please?05/31/21