How to create a chloropleth map from a given raster array and Lat Lon meshgrid arrays?

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I have a raster array (R), a shapefile (District_Boundaries.zip), and lat lon meshgrid arrays (LatGrid.mat and LonGrid.mat). How to create a chloropleth map out of the mean for the given sub regions of the shapefile? I have attached all the files with this question.
The raster array is:
R=rand([604 584]);
Kindly help me with it.

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