## 3 Results and Discussion
### Determination of the Representative Sample  
In the research proposed by [PERSON] (2019), the regional average method of 5 points was used with the electromagnetic densimeter to evaluate the repeatability and consistency of asphalt mixture density measurements in pavements. The results showed a high consistency, since the standard deviation was less than 0.25%. Subsequently, 14 cores were extracted, whose densities were evaluated and compared with the single reading method (one reading per point). The single-reading method showed a better statistical distribution than the five-reading method in the pavement points analyzed. This suggests that the  
Figure 8: HMA density results of the 34 JMF in Segment 3.  
Figure 7: HMA density results of the 5 JMFs in Segment 2.  
variation in asphalt mixture density within the area analyzed significantly exceeded the repeatability threshold set out in the protocol [38]. Equation (5) was used to obtain a representative sample:  
\[s=\frac{N}{(N-1)*K^{2}+1} \tag{5}\]  
where the small sample size (\(s\)) of the total data population (\(N\)), and the margin of error (\(K\)), which are usually 5% to 10%, indicate that the results obtained from the sample will have an accuracy of 5% or 10%, respectively. For this analysis case, the result of 5% was 237 data (40.6%), and for 10%, it was 86 data (14.6%); after this, a geometric average was made and this was 162 data (27.6%), so that the sample population of data to be analyzed was close to 162.  
For the case study of this research, it was possible to take a representative sample of 24.9% of the total readings, which was obtained by the intentional stratified statistical sampling method, of which the density standard deviation presented by the data families was set as the central value. AASHTO T343 states that the permissible standard deviation for asphalt mixtures should be 0.050 g/cm\({}^{3}\). Data families were selected to meet this by reducing the population to six working formulae of asphalt mixtures (JMF).  
In order to analyze the 586 readings, it was considered that the mixtures had to meet a minimum of 10 reading data at different points and the standard deviation of the field density data had to be less than 0.050 g/cm\({}^{3}\) (less than 1.2% in percentage data, such as percentage of compaction and air voids).  
This process is carried out according to the test method for HMA density in the field using electronic contact devices by the AASHTO and that adaptation is being sought by the Mexican Institute of Transport (IMT) to replicate this function Mexico, which they use as a standardization parameter through a correlation factor of the device readings that must have at least 5 test specimens and that the standard deviation of the readings is less than or equal to 0.050 g/cm\({}^{3}\) for the equipment to be accepted with readings homogeneous, consistent, and does not require an adjustment factor [25].  
Therefore, 6 job mix formulae were chosen, which met the conditions of population consistency--JMF41 (21 data), JMF19 (10 data), JMF23 (60 data), JMF10 (13 data), JMF17 (28 data), and JMF34 (14 data)--giving a total of 146 data in 6 JMF.  
Figure 9 shows the density data of asphalt mixtures by JMF, showing only those that met the parameters of statistical repeatability described in the previous paragraph.  
Figure 9: Field density results of HMA with the EM density gauge of the job mix formulae with statistical consistency separated by location distance: JMF41, JMF19, and JMF23 in Section 1 (**a**); JMF10, JMF17, and JMF34 in Section 3 (**b**).  
The observed data of the standard deviation (\(\sigma\)) of the job mix formulae that indicate repeatability are JMF41 \(\sigma\) = 0.025, JMF19 \(\sigma\) = 0.025, JMF23 \(\sigma\) = 0.025, JMF10 \(\sigma\) = 0.021, JMF17 \(\sigma\) = 0.024, and JMF34 \(\sigma\) = 0.027.