The tournament was 4 rounds, as shown in the cross table, meaning that a plus score is 2.5 or greater, an even score is 2.0, and a minus score is 1.5 or less.
I’m pretty sure I understand how Modified Median works, but I’ll work through the first player here by hand. The background:
34E1. Modified Median
The Median system, also known as the Harkness system for inventor Kenneth Harkness, evaluates the strength of a player’s opposition by summing the final scores of his or her opponents and then discarding the highest and lowest of these scores.
In the Modified Median system, players who tie with even scores (an even score is equal to exactly one half of the maximum possible score), have the highest- and lowest-scoring opponents’ scores excluded. The system is modified for players with non-even scores to disregard only the least significant opponents’ scores: the lowest-scoring opponent’s score is discarded for tied players with plus scores and the highest-scoring for tied players with minus scores.
For tournaments of nine or more rounds, the top two and bottom two scores are discarded for even-score ties, the bottom two scores for plus-score ties, and the top two scores for minus-score ties.
These scores are adjusted for unplayed games, which count a half point each, regardless of whether they were byes, forfeits, or simply rounds not played after an opponent withdrew. So an opponent who won the first two games, lost the third, withdrew and did not play rounds four or five would have an adjusted score of 3 points (1+1+0+0.5+0.5 = 3). These adjusted scores are used only to calculate the opponent’s tiebreaks. The player’s own score is not changed.
If the player involved in the tie has any unplayed games, they count as opponents with adjusted scores of 0.
(This is consistent with the video you linked at 12:56-18:35).
So the first player, Peter McKinnie, has 4.0 points, which is a plus score in a 4 round tournament. They played opponents 13, 7, 4, and 2 (using the numbers from the online xtable; these are 8, 7, 4, and 2 in the screenshot).
Opponent 13 has a score of 1.5, but 1.0 of that is from a full point bye, so adjusting that down to 0.5 for the unplayed game leaves a score of 1.0 points. Opponent 13 is going to get tossed out anyway.
Opponent 7 has a score of 2.0 with all games played.
Opponent 4 has a score of 2.5, with 0.5 from a half point bye (so no adjustment needed).
Opponent 2 has a score of 3.0 with all games played.
So the Median tosses high and low, leaving 2.0 + 2.5 = 4.5.
Solkoff doesn’t toss any scores, leaving 1.0 + 2.0 + 2.5 + 3.0 = 8.5.
Modified Median should toss only the low score for a player with a plus score, resulting in 2.0 + 2.5 + 3.0 = 7.5.
Cumulative (since it’s shown) would be 1 + 2 + 3 + 4 = 10.
Cumulative of opposition would be (0 + 0 + 1 + 1.5 - 1) + (1 + 1 + 1 + 2) + (0.5 + 1.5 + 1.5 + 2.5 - 0.5) + (1 + 2 + 3 + 3) = 2 + 5 + 5.5 + 9 = 1.5 + 5 + 5.5 + 9 = 21.
All of those hand calculations match the display from WinTD above, other than for Modified Median, and again note that Modified Median should be between the Median (tossing high and low opponent scores) and Solkoff (not tossing any opponent scores) in all cases, which it isn’t here.
