Weighted geometric mean
The weighted geometric mean is a way to find the middle value of some numbers. It’s like finding the average or the most common number, but it takes into account how important each number is.
For example, let’s say we have some numbers: 2, 5, and 6. We can find the regular average by adding them up and dividing by how many there are: (2+5+6)/3 = 4.33. That’s the middle number.
But what if we want to give more importance to some numbers than others? For instance, what if we want to prioritize the biggest number, 6, and care less about the other two? To do that, we use the weighted geometric mean.
The first step is to multiply each number by a weight, which tells us how important it is. For example, we may decide to assign a weight of 1 to 2, a weight of 2 to 5, and a weight of 3 to 6. This means that we care about 6 more than the other values, so it will have more impact on the final result.
Next, we multiply each number by its weight:
2 x 1 = 2
5 x 2 = 10
6 x 3 = 18
Then, we multiply all the weighted numbers together:
2 x 10 x 18 = 360
Finally, we take the n-th root of that number, where n is the total number of weights we have used. In this case, we had three numbers with different weights, so n=3:
360^(1/3) = 6.16
That’s the weighted geometric mean. It’s the middle value that takes into account how important each number is. In this case, because we gave more importance to 6, the result is closer to 6 than to the other numbers.
For example, let’s say we have some numbers: 2, 5, and 6. We can find the regular average by adding them up and dividing by how many there are: (2+5+6)/3 = 4.33. That’s the middle number.
But what if we want to give more importance to some numbers than others? For instance, what if we want to prioritize the biggest number, 6, and care less about the other two? To do that, we use the weighted geometric mean.
The first step is to multiply each number by a weight, which tells us how important it is. For example, we may decide to assign a weight of 1 to 2, a weight of 2 to 5, and a weight of 3 to 6. This means that we care about 6 more than the other values, so it will have more impact on the final result.
Next, we multiply each number by its weight:
2 x 1 = 2
5 x 2 = 10
6 x 3 = 18
Then, we multiply all the weighted numbers together:
2 x 10 x 18 = 360
Finally, we take the n-th root of that number, where n is the total number of weights we have used. In this case, we had three numbers with different weights, so n=3:
360^(1/3) = 6.16
That’s the weighted geometric mean. It’s the middle value that takes into account how important each number is. In this case, because we gave more importance to 6, the result is closer to 6 than to the other numbers.
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