A bit of cartographic jargon, referring to a class of data values which are actually measurements of volume. When several of these measurements are collected for the purpose of representing a geographic distribution on a map, special care must be taken to represent them accurately.
Volumetric data are necessarily quantitative, but not all quantitiative data are volumetric. It can be tricky recognizing which ones are which. Obviously, things that use volume units (like cubic meters) are volumetric. Less obviously, massurements that use mass or weight units are volumetric. A good rule of thumb is that if a "density" measurement (the original measurement per unit area) is meaningful for the original measurement, the latter is volumetric.
The following geographic distributions are volumetric:
- Population and other counts of discrete phenomena, collected for discrete areas
- Crop Yields, in tons
- Carbon dioxide emissions (or hot air emitted by politicians), in tons, by state
- Oil production, in barrels
- Topsoil loss, tons
The following geographic distributions are not volumetric:
- Density of any volumetric distribution (unit per square mile)
- Median income by state
- Annual Rainfall, in centimeters
You may find it difficult to believe that the population of, say, the United States is a volume, but it is. Imagine for a moment that you have one marble for each person in the United States (If you want to do this in your basement, use grains of sand). Now imagine a box big enough to hold all of the marbles. A rectangular box will do, but let's use a specially-shaped box, with vertical sides, and whose horizontal cross-section is shaped the same as the United States. Now start dropping the marbles in the box, one by one. The marbles will soon cover the bottom of the box and begin to pile up. Let's say that, given ideal packing, a marble will take up 1 cubic centimeter including interstices. That's about 300,000,000 cubic centimeters. It's not hard to see how the marbles are a volume, and the direct correspondence of one marble to one person shows how the population is a volume, too.
Now dump out the box and insert vertical partitions whose horizontal cross-sections resemble the borders between the states. The box will have 51 pigeonholes, each shaped like a particular state, and in cross-section, all 50 states (plus DC) will be represented proportionally. Start dropping the marbles into the box again, but this time, drop exactly the number of marbles into a particular partition as the population of the corresponding state. The partition for Maryland will get about 5,000,000 marbles, the partition for California will get about 30,000,000 marbles; the partition for the District of Columbia will get about 550,000 marbles. So, the partition for California will contain about 30,000,000 cubic centimeters of marbles; the partition for DC about 550,000 cubic centimeters of marbles. But if you add up all 51 partitions you will still have 300,000,000 cubic centimeters of marbles.
If you wanted to make a choropleth map of United States population by state, you'd have a problem, of course. If you chose a shade for each state directly proportional to its total population, that would be equivalent to filling the California partition to a depth of 30,000,000 marbles and the DC partition to a depth of 550,000 marbles. The California partition uses up far, far more marbles than it should proportionately to the DC partition. On the map, humans are able to visually multiply a fill shade by the area that's filled in to get an impression of the total value. When the shades are proportionate to a volumetric value, (e.g. total population), large areas are represented out of proportion to smaller areas.
You really have only two choices when representing volumetric data on a map: