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I am attempting to create a point that scales in relative size to a particular integer (frequency) and is gradiented to a particular integer value, and then overlay that point onto each specific polygon of a shapefile (USA)

The point should look something like this where darker colored points denote higher numbers and larger circles denote higher frequencies.

enter image description here

I have frequencies all values (included frequencies) joined to the USA shapefile, but am unable to create the points.

Are they buffers?

I'm new at this (QGIS).

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I'd suggest a centroid marker with a data-defined size as shown in the following screenshot. Additionally, you will also want to set a data-defined color.

Here's an updated screenshot which shows the expression to control the alpha of the point fill. Adjust the 2nd and 3rd parameter to your data. Read the function documentation in the expression builder for how to.

enter image description here

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In Qgis, you can find a "Diagram" tab under the properties of the layer. If you enable the "Display Diagram" option, you should be able to add a diagram to each spatial unit you have in your shapefile. Off course, don't forget to choose an attribute to scale your diagrams as shown below. Propotional symbol map

Don't hesitate also to explore other possibilities of this nice tools (proportional symbol law, position of the symbols, ...).

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