I have a dataset containing 8 categories, I now want to visually compare the variance between the categories. The most common approach would be to use box plots or violin plots but I would like to know if there are other "more exciting" ways of doing that?
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In addition to the plot types you have mentioned (box plots and violin plots), you can visualize it for example as histograms, probability density functions, or kernel density estimates. It depends on your goal and your data. If you have relatively small dataset, you can also use scatterplots or strip plots, as suggested in other answers by @user233738 &@asdf - that way you can actually show all of the datapoints.
On the other hand, if you are only interested in variance (as you mentioned), but not in measures of central tendency (mean/median etc), you can also just show the numerical variance values in datatable.
You can also use strip plots or strip charts for comparing variance. They are similar to boxplots but "more exciting".
I often use a scatter plot when trying to visualize variance. The way I proceed is by plotting all data together, separating each of the groups by colour. Now you can compare dispersion along the equally-coloured points