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.