Weighted Average by Distinct Category

Hello PBI Community,

I'm fairly new to DAX and am trying to write a DAX formula to calculated weighted average by distinct category as follows:

The table structure is this:

Values for Total Sample and Average Size within Sample columns are grouped by category (i.e each rows with the same category will have the same value for those 2 columns). I am trying to calculate the folowing weighted average by distinct category.  For the data above, the result I would want is below:

[ (1400 x 14) + (300 x 30) ] / (1400+300) = 16.82 (This is the desired result). In a slicer if Place Name Indiana, Ohio and New Jersey are selected, I would want this value. The result will also be same if only Indiana and New Jersey are selected. If only Indiana and Ohio are selected (places with same category), I would not want to do any aggregation and only display the calucation as 14.

I have created a DAX formula below that does not take into account the distinct category which gives the below:

DIVIDE(
SUMX('Table','Table'[Total Sample]*'Table'[Average Size within Sample]),
SUM('Table'[Total Sample]))

Translates to:

[(1400 x 14) +(1400 x 14) + (300 x 30)] / [ (1400+1400+300)] = 15.54 (This is not the desired result)

Any help that can be suggested to modify the formula to get the desired result will be appreciated.

Thank you so much.