How to analyze statistical difference between averages of mode, mean and median?

Attached is the graph with my data:

I have 4 distributions of particles of different sizes. For each one of them, a particle size frequency distribution has been measured three times. Median, mean and mode were calculated for each frequency distribution and averaged for each of the four samples (types). The error bars in this graph are +/- one standard deviation from that averaging.

Looks easy, right?!

But then, how can I statistically test if the mean (and median, and mode) for 0X sample (type) is significantly different from the 10X sample (type) and from the other samples (types)?!

Running one-way ANOVA would work if these were not averages already. One-way ANOVA doesn't seem to take into account the fact that the mean, median and mode to be compared arose from averaging of these parameters from three repeats.

And that's where I am puzzled - which statistical technique to use for this kind of situation?!