Good catch. If there are n samples, and the lower half of them are equal to or less than 0.29, then a total mean of 0.82 would require that sum of the the upper half must be greater than 0.82n - 0.29n/2 = 0.675n. For n/2 numbers to sum to 0.675n, the mean of those numbers must be 1.35, which is decidedly above 100 %, proving at least one of the numbers must have been greater than 100 %.
It being a weighted average does sound like a reasonable explanation, though. A median of 0.29 and weighted mean of 0.82 is trivially possible given e.g. values (0.29, 0.29, 0.82) and weights (0, 0, 1).
It being a weighted average does sound like a reasonable explanation, though. A median of 0.29 and weighted mean of 0.82 is trivially possible given e.g. values (0.29, 0.29, 0.82) and weights (0, 0, 1).