As detailed in this answer on the math SE, weights in a weighted median are expressed duplicates of the datum. In your top example, replace the weights with their multiples of ten, like so:

            A       B     C     D     E     F
weights:    1       1     1     2     1     4
returns:    10%     20%   30%   1%    2%    1%

Sort these by return and you have 1 1 1 1 1 1 2 10 20 30; the median of this pseudo-dataset is the weighted median, in this case the average of the middle two values, i.e. 1%. If you repeat this exercise for the second set, you'll see that the value is 1.5%.

Also note that the weighted-median is the same for any vector of weights proportional to this one. (This is straightforward to prove, but I leave that to you.)

As detailed in this answer on the math SE, weights in a weighted median are expressed duplicates of the datum. In your top example, replace the weights with their multiples of ten, like so:

            A       B     C     D     E     F
weights:    1       1     1     2     1     4
returns:    10%     20%   30%   1%    2%    1%

Sort these by return and you have 1 1 1 1 1 1 2 10 20 30; the median of this pseudo-dataset is the weighted median, in this case the average of the middle two values, i.e. 1%. If you repeat this exercise for the second set, you'll see that the value is 1.5%.

Also note that the weighted-median is the same for any vector of weights proportional to this one. (This is straightforward to prove, but I leave that to you.)

As detailed in this answer on the math SE, weights in a weighted median are expressed duplicates of the datum. In your top example, replace the weights with their multiples of ten, like so:

            A       B     C     D     E     F
weights:    1       1     1     2     1     4
returns:    10%     20%   30%   1%    2%    1%

Sort these by return and you have 1 1 1 1 1 1 2 10 20 30; the median of this pseudo-dataset is the weighted median, in this case the average of the middle two values, i.e. 1%. If you repeat this exercise for the second set, you'll see that the value is 2%.

Also note that the weighted-median is the same for any vector of weights proportional to this one. (This is straightforward to prove, but I leave that to you.)

As detailed in this answer on the math SE, weights in a weighted median are expressed duplicates of the datum. In your top example, replace the weights with their multiples of ten, like so:

            A       B     C     D     E     F
weights:    1       1     1     2     1     4
returns:    10%     20%   30%   1%    2%    1%

Sort these by return and you have 1 1 1 1 1 1 2 10 20 30; the median of this pseudo-dataset is the weighted median, in this case the average of the middle two values, i.e. 1%. If you repeat this exercise for the second set, you'll see that the value is 1.5%.

Also note that the weighted-median is the same for any vector of weights proportional to this one. (This is straightforward to prove, but I leave that to you.)