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Panel data: Mean of DISTINCT population observation

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I have a "census" data set. Each row is the number of patients living in the specific housing area of a facility for the each day. I generated a total number of patient per day for the facility.

sort FacilityCode2 CensusDate2
by FacilityCode2 CensusDate2: egen DailyFacilityPopulation=total(InmateCount)

What I need next is to create the monthly average of patients per month (per facility). My try was:

bysort FacilityCode2 month : egen MonthlyAverage_FP=mean(DailyFacilityPopulation)

but I am including all the rows of my DailyFacilityPopulation variable and not only one number (it should be one number per day). I tried to generate a flag to select only one distinct observation but I dont know if it is working. At the end, I would only need one number per month (which is the monthly average of each facility)


Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input str4 FacilityCode2 int CensusDate2 float month str8 HousingArea byte PatientCount float DailyFacilityPopulation byte flag float MonthlyAverage_FP
"AMKC" 20454 1 "LOWER 8"  28 101 1 87.66666
"AMKC" 20454 1 "MOD 10 A" 23 101 0        .
"AMKC" 20454 1 "MOD17L A" 50 101 0        .
"AMKC" 20455 1 "RR"       15  51 1 87.66666
"AMKC" 20455 1 "3 TOP"    36  51 0        .
"AMKC" 20455 1 "LOWER 2"   0  51 0        .
"AMKC" 20456 1 "MOD 18UA" 49 111 1 87.66666
"AMKC" 20456 1 "MOD 7"    34 111 0        .
"AMKC" 20456 1 "LOWER 11" 28 111 0        .
"AMKC" 20485 2 "LOWER 4"  22  81 1 96.33334
"AMKC" 20485 2 "LOWER 5"  27  81 0        .
"AMKC" 20485 2 "MOD 12A"  32  81 0        .
"AMKC" 20486 2 "UPPER 17" 21  73 1 96.33334
"AMKC" 20486 2 "UPPER 14" 26  73 0        .
"AMKC" 20486 2 "UPPER 15" 26  73 0        .
"AMKC" 20487 2 "4 UPPER"  40 135 1 96.33334
"AMKC" 20487 2 "4 MAIN"   30 135 0        .
"AMKC" 20487 2 "3 MAIN"    5 135 0        .
"AMKC" 20487 2 "2 MAIN"   10 135 0        .
"AMKC" 20487 2 "1 MAIN"    0 135 0        .
"AMKC" 20487 2 "MOD 18UB" 50 135 0        .
end
format %tdnn/dd/CCYY CensusDate2
Thank you,
Marvin

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