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I am trying to map demographics data for a county in the UK based upon a combination of Census data. I want to compare the the averages for the county alone to the averages of the UK as a whole and display it using a sort of traffic lights symbology (red, orange, yellow, green, where red is way above average and green is way below average).

My problem is I'm not sure about what type of graduated symbology to use. Can someone please explain what Graduated Symbology is best to use in my situation?

I used Natural Breaks (Jenks) at first and was very happy with that but then I read on the ESRI website: "Natural Breaks (Jenks) are data-specific classifications and not useful for comparing multiple maps built from different underlying information." This makes me think using Jenks and then comparing the county averages to the national averages or comparing different categories (health data versus accessibility data) isn't appropriate.

So then I thought it would be best to use Equal Interval or Quantile symbology or define my own bands (split the results in four so I can assign colours to each 25%).

Any advice/help/information would be great.

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First, the stop light color scheme is not recommended because of red-green colorblindness. See Colorbrewer for a a more palatable set of color ramps. (FYI graduated symbology typically refers to icons that get larger to signify some numeric values, not changes in color used for choropleth maps.)

The other question, how to make the breaks across different categories, is more difficult. In the end you want to make each individual map interpretable, but want to maximize the ability to make comparisons between the maps. This may involve normalizing the data to be comparable, e.g. since you want to make comparisons to the national average mapping location quotients may be reasonable (which you might use a diverging color scheme for), or it may involve standardizing the choropleth scheme between maps. For example, if you had all proportion data you could have an equal interval color scheme for every 10%.

In this answer I discuss some research that suggests quantiles are good approach for cross map comparisons. This also has the side effect of approximately equal proportions for each color bin (assuming the polygons are approximately equal area) which can be a problem if you use other break schemes to classify all maps.

See Effectively displaying demographic data on a printed map for more discussion about displaying multiple demographic variables.

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