

































 
 

LEARNING PROCESS CONTROL MTsN 1 MEDAN 
 

Titin Rahmayanti Rambe1, Fasti Rola2, Siti Habsari Pratiwi3, 
Anggili Pratama4, Jhohas Dongoran5, Hasratuddin6 

1,2,3,4,5 DoctoralStudent at Medan State University 
6Doctoral Lecturer at Medan State University 

1e-mail:titinrahmayanti@stkipalmaksum.ac.id 
2e-mail:fastirola@usu.ac.id 

3e-mail:shihabpratiwi@iainlangsa.ac.id 
4e-mail: anggilipratama@gmail.com 

5e-mail: dongoran231089@gmail.com 
6email:siregarhasratuddin@yahoo.com 

 
Abstract.Abstract. The purpose of this study is to analyze whether the product produced by 
the process meets the initial expectations or meets the standards expected beforehand. The 
learning process is one that must be tested for execution and outcomes to ensure that the 
outputs meet the objectives and are of the appropriate quality. It would be very interesting 
to evaluate and explain the original incident on the basis of the authentic data collected, as 
well as how to present that data to interested parties and how the data is processed using 
appropriate statistics; this will give us an idea of how a process occurs. Therefore, the 
sample for this study consisted of valid National Exam (NE) results data for MTsN 1 Medan 
students from the academic year 2013/2014 to 2017/2018 in four subjects (Indonesian, 
English, Mathematics, and Science). The results of the study showed that the learning 
process that took place at the Medan MTSN 1 school in the academic year 2013/2014 to 
2018/2019 went smoothly. 
 
Keywords : Control, process, learning, NE, Medan 
 
Introduction 

The multivariate statistical approach is an analytical methodology that considers the 
correlation of a set of correlated criterion variables as a system. Researchers can use 
multivariate analysis to solve more generic or difficult issues, as well as challenges that more 
properly mirror the actual world. One of the goals of multivariate analysis is to discover and 
explain the underlying structure or properties of the data. Multivariate analysis is also used 
to find new variables that are less in number than the original variables but may explain 
fluctuations in the original variables. 

The control analysis of MTSN 1 Medan's learning processes and results is discussed in 
this article. The purpose is to establish if the product generated by the process satisfies its 
initial expectations or continues to satisfy the expected standards or original design for 
which it was built. The learning process is one that must be monitored for execution and 
results to ensure that the outputs fulfill the objectives and are of appropriate quality. 

It would be fascinating to explore the real occurrence of legitimate data, how to 
establish the data's significance, and how to analyze the data using relevant statistics to 
demonstrate how the process works in this context. As a consequence, valid student 
National Exam results (MTSN 1 Medan 2013/2014-2017/2018) are used in four courses 
(Indonesian, English, Mathematics, and Science). 

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mailto:titinrahmayanti@stkipalmaksum.ac.id
mailto:fastirola@usu.ac.id
mailto:sihabpratiwi@iainlangsa.ac.id
mailto:anggilipratama@gmail.com
mailto:dongoran231089@gmail.com


 
 

How may multivariate statistical approaches be used to investigate the links and 
interrelationships between the topics of Indonesian (IND), English (ING), and Science with 
Mathematics (MAT)? What are the consequences of the continuing learning process 
control? The goal of this article is to investigate and describe the relationships and 
connections between the subjects covered in the National Examination, as well as to 
provide interested parties with information on how to achieve learning process control 
results in MTsN 1 Medan by using multivariate statistical methods. 
 
Result and Discussion 

The sample for the analysis in this article is students' National Examination (MTsN 1 
Medan 2013/14-2017/18) results in four disciplines (Indonesian, English, Mathematics, and 
Science). Over the course of five years, the total number of data points on student scores 
from 1,734 people was discovered to be distributed as follows: in 2013/2014, there were 
294 people; in 2014/2015, there were 308 people; in 2015/2016, there were 378 people; in 
2016/2017, there were 355 people; and in 2017/2018, there were 399 people. 

The data analysis in this paper focuses on 1) the relationship between Indonesian, 
English, mathematics, and science training. The author chose the 2013/2014 
implementation year because he wanted to investigate and disclose more linked themes. 
The author chose the 2013/2014-2017/2018 National Examination with Indonesian, English, 
Mathematics, and IPAs for the whole five-year period. 2). Concerning the control of the five-
year learning process, the UN value data is sent through the control model 
UperControlLimit(UCL), 

 

Data Analysis for 2013/2014 

This section analyzes actual data from IndonesiaMTsN 1 Medanin 2013/2014 test results, 
especially four subject tests: Indonesian (X1), English (X2), Mathematics (X3), and Science 
(X4), with a total of 294 pupils. We acquired the following results by calculating the average 
of each: The following results were obtained from calculating the average of each: 
 

Table 1. Average of Four Subjects in Comparison 
SUBJECT ENG ING MATT IPA 

Jl 2405,400 2586,500 2414,300 2451,000 

Means 8,182 8,798 8,212 8,337 

Var 0.862 0.279 1,111 0.723 

Range 4,300 3,800 4,700 4,200 

Source: results of data processing by researchers, 2022 

 

Based on the analytical results in Table 1, the assumption is that the data is normally 
distributed and that the learning is done by the same teacher. The highest average score in 
English (ING) courses was 8.798; the lowest average score in Indonesian (IND) subjects was 
8.182. This demonstrates that the English subject has the highest student accomplishment, 
whereas the Indonesian language subject has the lowest. 

This section examines actual data from IndonesiaMTSN 1 Medanin test results from 
2013/2014, especially four subject tests: Indonesian (X1), English (X2), Mathematics (X3), 
and Science (X4), with a total of 294 pupils. We acquired the following results by calculating 

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the average of each: The following results were obtained from calculating the average of 
each: 

To see the relationship or correlation between topics, the following correlation matrix 
calculation results are presented: 
 

Table 2. Matrix of Variance-Covariance Correlation 
BIND 1.0000 0.2185 0.2952 0.1256 

BING 0.2185 1.0000 0.3581 0.3487 

MATE 0.2952 0.3581 1.0000 0.2867 

IPA 0.1256 0.3487 0.2867 1.0000 

 ENG ING MATT IPA 

Source: results of data processing by researchers, 2022 

 
The connection between English (ING) and mathematics (MAT) topics has the greatest 

value of 0.3581, while the correlation between IND and science subjects has the lowest 
value of 0.1256, according to the study shown in Table 2. This suggests that the strongest 
relationship between disciplines is between English and mathematics, whereas the poorest 
link is between Indonesian and science. When the whole correlation value is taken into 
account, the correlation value is positive. This proves that pupils do admirably in all courses. 

The following are the results of constructing the inverse correlation matrix to see which 
topics can best predict other subjects. 
 

Table 3. Matrix of Inverse Correlation 
ENG 1.1153 -0.1351 -0.2813 -0.0124 

ING -0.1351 1.2657 -0.3283 -0.3314 

MATT -0.2813 -0.3283 1.2660 -0.2135 

IPA -0.0124 -0.3314 -0.2135 1.1788 

 ENG ING MATT IPA 

Source: results of data processing by researchers, 2022 

 
Each diagonal member of the inverse correlation matrix is proportionately connected to 

the correspondence variable specified by regression, according to the study shown in Table 

3. Each diagonal element is obviously equivalent to to
�

����
,, where R is the multicorrelation 

coefficient between the other variables. According to the aforementioned computation, the 

greatest percentage value for MAT classes is 21%  (
�.������

�.����
), while the lowest percentage 

value for IND classes is 10.3% (
�.������

�.����
). This means that MAT is the topic most anticipated 

by other subjects, whereas IND is the subject least predicted by other subjects. 
The results of the predictive analysis of subject values using regression analysis, 

.�� = �� + ���(�, �). ���(�)��(� − ��). 

 
1. The magnitude of the expected value provided by each Indonesian value to the value of 

mathematics is is����� = 5,471 + 0,335���� 

 
Table 4. Indonesian Language Scores on Mathematics Scores Coefficient 

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Coefficientsa 

Model Unstandardized 
Coefficients 

Standardize
d 

Coefficients 

t Sig. 

B std. Error Beta 

1 (Constan) 5,471 .523  10,470 .000 

BIND .335 063 .295 5,279 .000 

a. Dependent Variable: Mathematics 

 
2. The magnitude of the anticipated value provided to the math score by each English 

score is����� = 1,924 + 0,715���� 

Table 5. English Scores on Mathematics Scores Coefficient 

Coefficientsa 

Model Unstandardized 
Coefficients 

Standardize
d 
Coefficients 

t Sig. 

B std. Error Beta 

1 (Constan) 1924 .961  2001 046 

BING .715 .109 .358 6,553 .000 

a. Dependent Variable: Mathematics 

 
3. The magnitude of the expected value for the value of Mathematics supplied by each 

value of Indonesian (IND), English (ING), and IPA is����� = 5,250 + 0,355���� 

Table 6. Coefficient of Natural Science Scores on Mathematics Values 

Coefficientsa 

Model Unstandardized 
Coefficients 

Standardized 
Coefficients 

Q Sig. 

B std. Error Beta 

1 (Constant
) 

5,250 .582  9017 .000 

IPA .355 .069 .287 5.113 .000 

a. Dependent Variable: Mathematics 

 
4. The magnitude of the predicted value given by each value of Indonesian (IND), English 

(ING), and IPA for the value of Mathematics is����� = 0,008 + 0,248���� +

0,500���� + 0,213���� 

 

Table 7. Coefficient of IND, ING, IPA Values on Mathematical Values 

Coefficientsa 

Model Unstandardized 
Coefficients 

Standardized 
Coefficients 

Q Sig. 

B std. Error Beta 

1 (Constant) 008 .992  008 .994 

SON .248 061 .219 4,070 .000 

ING .500 .114 .250 4,396 .000 

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IPA .213 .069 .172 3,070 002 

a.Dependent Variable: Mathematics 

 
Learning Process Control Analysis 

The data utilized for analysis in this topic runs from 2013/2014 to 2017/2019 for the 
subjects of Indonesian, English, Mathematics, and Science on national exam scores.MTsN 1 
Medan. The first stage of process control analysis is to determine the determinant value of 
the covariance matrix, and the following data are obtained: 
 

Table 8. Determinants of the Covariance Matrix and UCL Values 

Year MDK0 UCL2 UCL3 

2013/2014 0.128366 44.62798 99.86698 

2014/2015 3.680986 44.62798 99.86698 

2015/ 2016 17.2321 44.62798 99.86698 

2016/ 2017 1.01308 44.62798 99.86698 

2017/ 2018 1.675714 44.62798 99.86698 

Source: results of data processing by researchers, 2022 

 

 
Figure 1. PBM Variability Control 

 

Table 9. Values – Chart for Future Sub Samples Means and UCL Values�� 
Year T^2 UCL2 UCL3 

2013/2014 78,459 223.1399 499.3349 

2014/2015 74019 223.1399 499.3349 

2015/ 2016 24,564 223.1399 499.3349 

2016/ 2017 24,862 223.1399 499.3349 

2017/ 2018 24.76 223.1399 499.3349 

Source: results of data processing by researchers, 2022 

 

0

20

40

60

80

100

120

2013/2014 2014/2015 2015/2016 2016/2017 2017/2018

Kontrol Variabilitas PBM

MDK0 UCL2 UCL3

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Figure 2. Variability Control of PBM 

 

Both the variability control lines and the process achievement control lines (T2) are 
below the UCL(2) and UCL(3) lines, according to the examination of the preceding tables and 
figures. This shows that the learning process has been running efficiently during the last five 
years in accordance with the learning outcomes provided. Thus, without lowering the 
amount of time variables required, the National Examination score data from 2013/2014 to 
2017/2018 may be used as a controller for the learning process. From the graph above, it 
can be concluded that the learning process that took place at the MTSN 1 Medan school for 
the 2013/2014 school year to 2017/2018 went smoothly as expected. 
 
Conclusion 
 
1. In general, the highest average student achievement score in the four subjects, namely 

Indonesian, English, Mathematics, and Natural Sciences, which were in the 2013/2014 
National Examination in MTs N 1 Medan, is 8.798 in the English (ING) subject, with a 
smaller standard deviation of 279; the lowest average student achievement score was 
8,182 in Indonesian (IND) lessons, with a standard deviation of 0.862. 

2. The weakest subject correlation, with a magnitude of 1256, is between Indonesian and 
IPA.The strongest correlation between these subjects, with a magnitude of 0.3581, is 
between English and mathematics.Indonesian and English have little or no correlation, 
as do Science and Mathematics.However, when the overall correlation value is 
considered, the data shows a positive correlation value. 

3. Mathematics is the subject most predicted by other subjects (21%), while Indonesian is 
the least predicted (10.3%). 

4. One subject's estimated value for another lesson (assuming there are no predictable 
lesson provisions). The results of the regression analysis used to forecast subject 

value,.�� = �� + ���(�, �). ���(�)��(� − ��) 
a) The magnitude of the expected value provided by each Indonesian value to the value 

of mathematics is����� = 5,471 + 0,335���� 
b) The magnitude of the anticipated value provided to the math score by each English 

score is is����� = 1,924 + 0,715���� 
c) The magnitude of the expected value assigned by each scientific value to the 

mathematical value is����� = 5,250 + 0,355���� 

0

100

200

300

400

500

600

2013/2014 2014/2015 2015/2016 2016/2017 2017/2018

Kontrol Capaian PBM

T^2 UCL2 UCL3

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d) The magnitude of the expected value provided to the value of mathematics by each 

BIN, ING, and IPA value is is����� = 0,008 + 0,248���� + 0,500���� + 0,213���� 
 

5. Based on the seven years of National Examination score data examined, from 2013/2014 
to 2017/2018, both the variability control lines (MDKov) and the PBM achievement 
control lines (T2) are lower than the UCL(2) and UCL(3) lines. This shows that the 
learning process has been running efficiently during the last five years in accordance 
with the learning outcomes provided. Thus, without lowering the amount of time 
variables required, the National Examination score data from 2013/2014 to 2017/2018 
may be used as a controller for the learning process. 

 
 
Bibliography 
 
Djauhari, Maman A. 2005. Improved Monitoring of Multivariate Process Variability. 

Journalsof Quality Technology.Wisconsin: American Society for Quality 

Djauhari, M.A., dan Dyah E. Herwindiati. 2022. Kontrol Kualitas Proses Kompleks. ITB Press: 
Bandung. 

Hasratuddin. 2019. Weakness Analysis Learning Mathematics Junior High School in Medan. 
Journal international of Mathematca. ISSN: 2456-8538Volume 02 |Issue 08 |August 
2019 p. 1-18. 

Johnson, Richard A. 2002. Applied Multivariate Statistical Analysis (5th). New Jersey: 

PersonEducation International. 

Whittaker, Joe. 1996. Graphical Models in Applied Multivariate Statistics. New York: 

John Wiley & Sons 

 
 

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	LEARNING PROCESS CONTROL MTsN 1 MEDAN
	Figure 2. Variability Control of PBM

