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I would like to create a choropleth that shows eligible voters per constituency. This data is in raw count.

How do I normalize the data in this case?

My intention is to show the difference in number of eligible voters for each constituency.

One thing I have done is shown how much each constituency deviates from the average. In some cases this is extreme and I have a range of variation between - 99% and 328%, so also having trouble representing this properly in buckets.

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I don't think you want to normalize your data, I believe what you are trying to do is standardize it. A commonly used method to do this would be using a z-score, which will standardize any data set in terms of the data sets mean and standard deviation. Here is a link to a Wikipedia article with the details:

Z Scores

Once you have converted your data to z scores the data will have a mean value of zero and a standard deviation of 1, which should make it easier to analyze and map. For example, since your data will be expressed in standard deviations any value between -1 and 1 is (roughly) average.

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