# How to normalize choropleth maps of census information?

I'm trying to improve on the census-based maps on this site, which shows census values at 5 scales from Collection Districts through to State.

Currently the maps show whole numbers (eg total population per polygon) which is not optimal. How should they be normalized?

Option 1: % of Total

I was advised to normalize by % of the total. This results in legend ranges such as "0.0004% to 0.0006% of the Total Population" which (IMO) make the legend hard to decipher - it's not an intuitive fraction, and is hard to put into perspective.

Option 2: Population Density

Another option could be to normalize based on area. Since the datasets are stored in meters, this also results in values like "0.000000019 to 0.000000035 persons per square meter".

I could flip this to show "area / person" - but this wouldn't make sense for datasets such as housing. And would it be offensive when applied to datasets such as religion (1km2 per X person)?

Is there a standard methodology to convert either of these values into something more meaningful? What do other people do on their census maps?

Thanks, Steve

• The solution to the problem of small densities is to change the units of measure. That's why population densities are usually expressed as people per square kilometer or square mile. And what exactly is the problem with mapping a housing density (or a density of any other count of discrete objects)? Using area/person is a creative approach--and for some datasets might be appropriate--but you have to be very, very clear with the legend and explanation, because most people will be unfamiliar with this approach. – whuber Jul 19 '11 at 13:39
• thanks for the tip, I'll change the unit of measure and will use this for housing and other densities. – Stephen Lead Jul 20 '11 at 0:06

Going with the % option, you could simply say "4 to 6 people in every million (1,000,000)" which means the same thing, but deals with nice round numbers (well, you're normalising to 1,000,000).

• I guess this is the same as @whuber's suggestion to change the units of measure, but since you put it as an answer, you get the tick. Thanks everyone. – Stephen Lead Jul 20 '11 at 0:05

Usually, choropleth maps display densities and not populations. Displaying population makes the result too dependent on the subdivision. So, option 2 is certainly the most appropriate one.

To define the density classes, this document describes common methodologies. The quantile method is usually applied for choropleth maps.

It depends on what you want to convey. Percent of total is useful if you want to show the relation to the whole country. Density is useful if you intend to show how the population is distributed on in relation to the physical geography. You could normalize by number of schools if education was important.

I frequently favor standard deviations when making comparisons across many geographic areas particularly when the mean and/or median is significant indicator. They can be intimidating to average users but can be expressed in terms of average, below average and above average. Another advantage is that it retains meaning at different levels of geography.

I agree with jul that density is more meaningful for your map of 'where Australians live'. But, I would take a page from Tufte's book and show the data. Label the areas with the population count while using the chloropleth to show density. A bunch of blues shapes of various shades can give a quick impression of the distribution and the legend will tell them how the shades relate. But, people get a lot more out of seeing the actual number. Nobody can make an intuitive leap from dark blue and big to really high density very quickly. Give them a the number and it will tie it all together.

If you can't work out the labeling, pop-ups or a separate table can work, too.

• Thanks Sean - great advice. I'm currently doing just that - the legend shows (or will show) the density while a popup shows the exact total. – Stephen Lead Jul 20 '11 at 0:02