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I've been having a very hard time finding a good representation (visual or analytical) for lots of data points on a very small, discrete scale. e.g. given a set of results from 1 to 5 in increments of 1.0, all the traditional approaches I've tried to break down that data result in very non-actionable results.

  1. The discrete nature of the data points makes the median virtually useless, as whatever the result is takes up 25% of the result space (lowest is 1.0, highest is 5.0), which leads me to use the mean instead.
  2. I tried using some form of box-and-whisker plot (substituting the useless median for mean) to visualize the data, but here the top quartile and the bottom quartile often coincide with the lowest and highest data points, completely robbing the chart of value.

I'm currently using a weighted scatter plot to visualize the results, but I feel like there should be a more effective method of distilling the data - as well as a numerical representation that doesn't rely on size perception to get the point across.

(Despite the similarities, I'm not actually dealing with ratings and I don't have an option of changing the nature of the data. These are AP scores from the College Board. Generally ratings are intended to be compared across items so you can get away with using the count-weighted mean to rank datasets but my desire here is to visualize the data within a single dataset, e.g. not "how well did students do in Chemistry vs US History?" but rather "what more can we learn about the performance of students on the Chemistry exam?")

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You could try with a violin chart rather than box-and-whisker, this way you could compare the probability density of the data of all subjects together, and also visualize the distribution of scores of each exam. This is particularly useful to uncover multimodal shapes. Having a look to your scatter plot maybe would help to understand better your thoughts and needs.

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  • $\begingroup$ Thank you! I hadn't come across those before - I think it definitely would be an improvement over the box-and-whisker. It still has the issue with the default markers reflecting the median and the interquartile range, though. It would probably suffice for the visual representation, but I feel there is still something missing in terms of numerical summaries of the data to take the place of those values when dealing with discrete data. $\endgroup$ – Mahmoud Al-Qudsi Jan 30 at 0:51

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