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I have a series of data in which each value $(k_1, k_2, \dots, k_j)$ is an average of individual measurements $(x_1, x_2, \dots, x_i)$; the $k_j$ values are subdivided in different clusters. I am describing the dispersion of the data within each cluster by a median statistics based on the $k_j$ values.

Should I also add a measure of the dispersion of the $x_i$ measurements by adding a confidence interval for each $k_j$ value? I reckon this approach will tell me how accurate the $k$ values are, but it is statistically sound?

I cannot assume a normal distribution of the measurements so I cannot use the standard deviation (sometimes I get a SD larger than the mean); I assume the confidence interval can be just as informative without rely on normality assumptions. I would not like to use again a median-interquartile range statistics approach because when plotting, drawing hundreds of points is fine, drawing hundreds of box-whiskers is simply too confusing.

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In my opinion adding dispersions (lines) always help. I would proceed plotting the upper and lower confidence interval as lines (or points) around your k points. Then you'd get three lines. To make it a bit more fancier I would plot an area delimited by the upper and lower CI boundaries (or maybe with a transparency/alpha level added to the RGB value) with the line of k point overlapped. In R you could produce the area plot with the polygon function and adding a fourth element to rgb(1, 0, 0, alphaValue) where alphaValue = .6 you'd create a red which is transparent. In matlab you can do the same but I do not remember the function call by heart.

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