Make numbered grid overlay with different colours showing the frequency of data in QGIS

Question

I would like to create a grid overlay. Each grid cell should be numbered and showing frequency of some data using different colours. The grid is over a shapefile of an area.

Answer 1

1. Find Create polygon graticule algorithm in processing toolbox (you have to install SAGA GIS before see: Enabling SAGA in QGIS?). Set the Output extent, Division Width and Division Height on the Parameters panel. Output extent should be a bit larger than the extent of the point layer. Each polygon will have three attributes: ID, ROW and COL in the new Rectangle graticule layer.
2. I suppose you have point data (if you have polygons generate centroid to work with points). From the vector menu choose Analysis Tools -> Count points in polygon You get a new Count layer, which is a copy of the graticule layer but a new column (NUMPOINTS) is added to the attribute table with the number of point in each polygons.
3. Create a thematic map based on the NUMPOINTS column of the Count layer. Customize the the number of classes, colors, etc.

Answer 2

Additionally I may suggest implementing the following workflow

Step 1. Create grid with Vector > Research Tools > Create Grid..., use the Point Extent as a Grid extent. For more details check the QGIS documentation.

Step 2. Apply one of the approaches described in these threads Calculating point layer values within polygon features in QGIS 2 or Updating field to give count of points in polygon using STIntersects?. The KISS principle will lead you to applying @TeddyTedTed's answer, e.g. 'Join attributes by location (summary)'

Step 3. Proceed with RMC > Symbology > Graduated, actually what @Zoltan defined as Step 3 in his answer.

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References:

• QGIS Tutorials and Tips | Performing Spatial Joins (QGIS3)