I have a set of data that follows a lognormal distribution (it is fixed-distance, variable-speed situation https://stats.stackexchange.com/a/23130/55305). I am trying to summarize the data in a single value and I would normally expect to use the harmonic mean. However, a co-worker suggested that a median might be a better measure.
I can't think of an argument for or against using the median to summarize the data ("average") versus using the harmonic mean. What are some things I should consider? Which will tell me what that the other won't?
As a note, I'm already capturing the mean and SD of the log of the values so that I can plug them into Wolfram Alpha for graphing (https://www.wolframalpha.com/input/?i=LogNormalDistribution[μ,σ]), but those data don't tell a human, at a glance, how fast or slow the system is on "average" since they are log values.