Could you please post the code that produces this output?
First obtain the data from
ColorData["HTML", "ColoRules"]
and eliminate duplicate colors. Then loop through the distance measures built-in for ColorDistance:
For each of these, check the four properties listed in the table above (see Metric -- from Wolfram MathWorld and distance[a,b] > 0 for all a != b), collecting pertinent information.
Afterwards, summarize the results in a Table[], using Histogram[] to produce the charts in the last row.