Integer programming formulations applied to optimal allocation in stratified sampling 5. Final remarks

In this paper we provided two new formulations leading to the achievement of the global minimum in multivariate optimum allocation problems. These exact integer programming formulations can be efficiently implemented using off the shelf free software (namely the R g l p k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamOuaiaadE gacaWGSbGaamiCaiaadUgaaaa@3B0D@ R package). In addition, the proposed formulations enable the definition of minimum sample sizes per strata, something which is clearly of interest in practice to avoid allocations with sample sizes less than 2, for example, which would lead to difficulties regarding variance estimation. Such minimum sample sizes may be set at larger values (say 5, 10, 30 or some other number) to ensure that the samples are large enough to tolerate some nonresponse or to ensure estimation is feasible for each stratum, if the strata are used as estimation domains.

The proposed approach improves upon the existing methods by tackling the allocation problem directly, and dealing with the non-linearity of either the objective function or the constraints, as well as the requirement that the solution provides only integer sample sizes for the strata. In the literature, previously existing methods tackle the problem with approaches which are not guaranteed to reach the global optimum, or that produce real-valued allocations that must be rounded to integer-values.

In practice, finding real-valued allocations is not a big problem, unless the stratum population sizes N h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaWGObaabeaaaaa@3860@ are very small or when there is a very large number of strata. In the first case, sampling one unit more, or less, can make a big change in the sampling fractions, which can cause some large impacts in the variances. In the second case, rounding the allocated sample sizes can make a difference in the total sample size n . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamOBaiaac6 caaaa@3819@ When all the stratum population sizes N h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaWGObaabeaaaaa@3860@ are relatively large, and the number of strata is reasonable, rounding non-integer sample sizes will not create a problem.

In this paper we carried out some limited numerical work, aimed essentially at demonstrating the feasibility of the proposed approach. The results obtained using Formulation C of the proposed approach are comparable to those achieved using the Bethel method, while providing integer-valued allocations that correspond to the global optimum. But given that only little differences were found between the two methods (BSSM and Bethel) in the applications considered, there may be little incentive to move to the BSSM method. The results obtained under Formulation D showed modest improvements over the textbook method used in the comparison.

Further research is needed to test the approach for larger problems and to assess its merits compared to other methods under other practical scenarios. An important advantage of the proposed approach is that both formulations can be implemented using off the shelf software, as indicated.

Acknowledgements

This research was supported by FAPERJ. Research Grant E-26/111.947/2012.

Appendix A

Description of the survey populations considered in the numerical experiment

Table A1
Description of the populations
Table summary
This table displays the results of Description of the populations. The information is grouped by Population (appearing as row headers), Description and Survey Variables XXXX (appearing as column headers).
Population Description Survey Variables ( y ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaWaaeWaaeaaca WG5baacaGLOaGaayzkaaaaaa@3B28@
CoffeeFarms Coffee farms in the state of Paraná, Brazil, from 1996 Agricultural Census. Number of Coffee Trees
Total Farm Area
Coffee Production
SchoolsNortheast Data from the 2012 census of schools, by school, for schools in the Northeast region of Brazil. Number of classrooms
Number of employees
MunicSw Information about Swiss municipalities from the package SamplingStrata. MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaam4uaiaadg gacaWGTbGaamiCaiaadYgacaWGPbGaamOBaiaadEgacaWGtbGaamiD aiaadkhacaWGHbGaamiDaiaadggacaGGUaaaaa@4639@ Area of Farming
Industrial Area
Number of Households
Population

 

Table A2
Stratification of the populations
Table summary
This table displays the results of Stratification of the populations. The information is grouped by Population (appearing as row headers), Stratification (appearing as column headers).
Population Stratification
CoffeeFarms Stratified considering the Number of Coffee Trees variable, using the Kozak algorithm available in the S t r a t i f i c a t i o n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaam4uaiaads hacaWGYbGaamyyaiaadshacaWGPbGaamOzaiaadMgacaWGJbGaamyy aiaadshacaWGPbGaam4Baiaad6gaaaa@45A1@ package.
SchoolsNortheast Twelve strata were formed considering: school type (4 classes), and school size - number of students (3 classes). School size stratification was performed using k   −   means MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaam4Aaiaayk W7cqGHsislcaaMc8UaaeyBaiaabwgacaqGHbGaaeOBaiaabohaaaa@422D@ clustering algorithm within each school type.
MunicSw This population is available from the S a m p l i n g S t r a t a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaam4uaiaadg gacaWGTbGaamiCaiaadYgacaWGPbGaamOBaiaadEgacaWGtbGaamiD aiaadkhacaWGHbGaamiDaiaadggaaaa@4587@ package and the strata correspond to regions of Switzerland.

 

Table A3
Number of strata, number of survey variables and total size for the survey populations considered
Table summary
This table displays the results of Number of strata. The information is grouped by Population (appearing as row headers), XXXX (appearing as column headers).
Population H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamisaaaa@396E@ m MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamyBaaaa@3993@ N MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamOtaaaa@3974@
CoffeeFarms 3 3 20,472
SchoolsNortheast 12 2 75,084
MunicSw 7 4 2,896

 

Table A4
Population summaries per stratum −   C o f f e e F a r m s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaeyOeI0IaaG PaVlaadoeacaWGVbGaamOzaiaadAgacaWGLbGaamyzaiaadAeacaWG HbGaamOCaiaad2gacaWGZbaaaa@42DE@
Table summary
This table displays the results of Population summaries per stratum −   C o f f e e F a r m s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaeyOeI0IaaG PaVlaadoeacaWGVbGaamOzaiaadAgacaWGLbGaamyzaiaadAeacaWG HbGaamOCaiaad2gacaWGZbaaaa@42DE@ . The information is grouped by Summary (appearing as row headers), XXXX and Stratum
XXXX (appearing as column headers).
Summary Stratum
h = 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B4F@ h = 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B4F@ h = 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B4F@
N h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamOtamaaBa aaleaacaWGObaabeaaaaa@3A8D@ 17,821 2,440 211
Y ¯ 1 h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGabmywayaara WaaSbaaSqaaiaaigdacaWGObaabeaaaaa@3B6B@ 4,291 26,688 218,712
Y ¯ 2 h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGabmywayaara WaaSbaaSqaaiaaikdacaWGObaabeaaaaa@3B6C@ 22 84 488
Y ¯ 3 h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGabmywayaara WaaSbaaSqaaiaaiodacaWGObaabeaaaaa@3B6D@ 2,671 13,204 129,033
S h 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaam4uamaaBa aaleaacaWGObGaaGymaaqabaaaaa@3B4D@ 2,873 15,541 193,366
S h 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaam4uamaaBa aaleaacaWGObGaaGOmaaqabaaaaa@3B4E@ 69 262 583
S h 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaam4uamaaBa aaleaacaWGObGaaG4maaqabaaaaa@3B4F@ 4,611 24,704 200,447

 

Table A5
Population summaries per stratum −   S c h o o l s N o r t h e a s t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaeyOeI0IaaG PaVlaadofacaWGJbGaamiAaiaad+gacaWGVbGaamiBaiaadohacaWG obGaam4BaiaadkhacaWG0bGaamiAaiaadwgacaWGHbGaam4Caiaads haaaa@47C9@
Table summary
This table displays the results of Population summaries per stratum −   S c h o o l s N o r t h e a s t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaeyOeI0IaaG PaVlaadofacaWGJbGaamiAaiaad+gacaWGVbGaamiBaiaadohacaWG obGaam4BaiaadkhacaWG0bGaamiAaiaadwgacaWGHbGaam4Caiaads haaaa@47C9@ . The information is grouped by Stratum (appearing as row headers), XXXX (appearing as column headers).
Stratum N h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamOtamaaBa aaleaacaWGObaabeaaaaa@3A8D@ Y ¯ 1 h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGabmywayaara WaaSbaaSqaaiaaigdacaWGObaabeaaaaa@3B6B@ Y ¯ 2 h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGabmywayaara WaaSbaaSqaaiaaikdacaWGObaabeaaaaa@3B6C@ S h 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaam4uamaaBa aaleaacaWGObGaaGymaaqabaaaaa@3B4D@ S h 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaam4uamaaBa aaleaacaWGObGaaGOmaaqabaaaaa@3B4E@
h = 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B45@ 82 45.1 54.0 309.2 24.9
h = 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B45@ 63 23.9 146.3 14.4 92.6
h = 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B45@ 7 80.9 700.4 29 342.5
h = 4 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B45@ 783 16.2 95.7 6.4 49.5
h = 5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B45@ 2,676 10.9 57.7 21.6 23.7
h = 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B45@ 3,958 6.1 26.7 4.2 17.9
h = 7 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B45@ 2,172 13.6 76.8 5.7 27.9
h = 8 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B45@ 45,243 2.5 9.3 3 8.8
h = 9 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B45@ 9,674 7.7 38.0 3.2 17.9
h = 10 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B45@ 1,743 17.3 49.1 9.2 36.7
h = 11 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B45@ 8,445 7.3 15.3 4.1 13.5
h = 12 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B45@ 238 37.7 140.8 18.4 88.9

 

Table A6
Population summaries per stratum −   M u n i c S w MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaeyOeI0IaaG PaVlaad2eacaWG1bGaamOBaiaadMgacaWGJbGaam4uaiaadEhaaaa@3F4F@
Table summary
This table displays the results of Population summaries per stratum −   M u n i c S w MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaeyOeI0IaaG PaVlaad2eacaWG1bGaamOBaiaadMgacaWGJbGaam4uaiaadEhaaaa@3F4F@ . The information is grouped by Summary (appearing as row headers), XXXX and Stratum
XXXX (appearing as column headers).
Summary Statum
h = 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B4F@ h = 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B4F@ h = 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B4F@ h = 4 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B4F@ h = 5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B4F@ h = 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B4F@ h = 7 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamiAaiabg2 da9iaaigdaaaa@3B4F@
N h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaamOtamaaBa aaleaacaWGObaabeaaaaa@3A8D@ 589 913 321 171 471 186 245
Y ¯ 1h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGabmywayaara WaaSbaaSqaaiaaigdacaWGObaabeaaaaa@3B6B@ 262.5 367.2 262.7 438.0 429.5 668.9 47.0
Y ¯ 2h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGabmywayaara WaaSbaaSqaaiaaikdacaWGObaabeaaaaa@3B6C@ 5.5 5.3 9.7 13.3 7.9 11.0 4.1
Y ¯ 3h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGabmywayaara WaaSbaaSqaaiaaiodacaWGObaabeaaaaa@3B6D@ 963.9 782.1 1,345.2 3,319.1 906.0 1,465.2 550.7
Y ¯ 4h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGabmywayaara WaaSbaaSqaaiaaisdacaWGObaabeaaaaa@3B6E@ 2,252.5 1,839.4 3,099.5 7,297.7 2,226.0 3,675.8 1,252.4
S h1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaam4uamaaBa aaleaacaWGObGaaGymaaqabaaaaa@3B4D@ 220.5 342.4 173.2 290.2 414.2 568.7 65.3
S h2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaam4uamaaBa aaleaacaWGObGaaGOmaaqabaaaaa@3B4E@ 15.1 13.0 19.4 29.7 14.9 15.5 8.2
S h3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaam4uamaaBa aaleaacaWGObGaaG4maaqabaaaaa@3B4F@ 4,600.9 2,794.7 5,003.5 14,610.0 2,178.6 2,802.1 1,197.5
S h4 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipu0de9LqFHe9fr pepeuf0db9q8qq0RWFaDk9vq=dbvh9v8Wq0db9Fn0dbba9pw0lfr=x fr=xfbpdbeqabeWaceGabiqabeqabmqabeabbaGcbaGaam4uamaaBa aaleaacaWGObGaaGinaaqabaaaaa@3B50@ 9,540.3 5,621.6 9,764.5 28,589.4 4,759.4 5,914.5 2,514.9

 

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