The other common method, graduated styling, is useful to show comparable attributes, effectively on interval and ratio scales. This method is type-specific, as we can only compare numbers directly. By using this method, QGIS creates intervals (bins), groups the attributes, links a color to every interval, and draws the features accordingly. We can apply graduated symbology to every geometry type, although the most common use cases are using a color ramp for shading polygons (choropleth map), and applying different icon sizes on points (proportional symbol map). First, let's apply a filter on our GeoNames layer (or its extract) to only show some of the settlements. With the following query we can filter only the seats of the administrative divisions:

    "featurecode" LIKE 'PPLA%'

Now we can apply a graduated symbology by doing the following steps:

1. Open the Style tab of our administrative boundaries layer.
2. Select the Graduated symbology.
3. Select a numeric column. Population density is a nice column to work with.
4. Select a color ramp (I used YlOrBr).
5. Select one of the familiar modes from styling rasters. Quantile works really well with population density.
6. Click on Classify, and apply the style.
7. Open the Style tab of our GeoNames layer.
8. Select the Graduated symbology and the population column.
9. For the symbology method, select Size.
10. Select a mode, and click on Classify. With population, Equal Interval is a good choice for creating initial intervals and modifying them to some more appealing ranges:

The custom ranges should always depend on the properties of the mapped data. For mapping settlements in Hungary excluding the capital city, I usually use intervals as per the preceding screenshot.