Pembelajaran Teorema Limit Pusat Melalui Simulasi

Authors

  • Joko Sungkono Universitas Widya Dharma Klaten
  • Andhika Ayu Wulandari Universitas Veteran Bangun Nusantara

DOI:

https://doi.org/10.32585/absis.v4i2.2520

Keywords:

Central Limit Theorem, R Software, Sampling Distribution, Simulation

Abstract

The mathematical learning of the central limit theorem has been widely discussed in scientific writings by researchers through various versions of proofs. The discussion of the central limit theorem in case application has also been carried out with many different cases. However, students need to be given an overview of the truth of the central limit theorem through a general application. The truth and accuracy of the central limit theorem can be studied through a simulation study. Through simulation with R software, students can perform parameter variations such as variations in the population distribution, variations in the sample size used, as well as the number of repetitions or replications in studying the central limit theorem. The accuracy of the central limit theorem through simulation is determined by looking at the trend of the sampling distribution of the mean sample in the form of a histogram. The simulation results state that, in general, the larger the sample size used, the closer the sampling distribution to the mean sample is to the normal distribution. For samples taken from a population that has a distribution that is closer to symmetrical, then for a sample size that is not too large, the distribution of the mean sample is closer to a normal distribution. However, for samples originating from an asymmetric distribution, a larger sample size is required to obtain a sample mean that is close to the normal distribution

Author Biography

Joko Sungkono, Universitas Widya Dharma Klaten

Sinta ID: 6087637

References

Arsham, Hossein. 2020. “System Simulation: The Shortest Route to Applications.” 2020. http://home.ubalt.edu/ntsbarsh/simulation/sim.htm.

Bain, L.J., and Engelhardt, M. 1992. Introduction to Probability and Mathematical Statistics. 2nd ed. California: Duxbury Press.

Budiharto, Widodo, and Ro’fah Nur Rachmawati. 2013. Pengantar Praktis Pemrograman R Untuk Ilmu Komputer. Jakarta: Halaman Moeka. http://socs.binus.ac.id/files/2016/06/Pengantar-Praktis-Pemrograman-R-untuk-Ilmu-Komputer.pdf.

Dekking, F.M., C. Kraaikamp, H.P. Lopuhaa, and L.E. Meester. 2006. A Modern Introduction to Probability and Statistics: Understanding Why and How. Journal of the American Statistical Association. Vol. 101. Netherlands. https://doi.org/10.1198/jasa.2006.s72.

Hartanto. 2016. Pengenalan Analisis Statistik Dengan Software R. Yogyakarta: Magnum Pustaka Jaya.

Hays, William L. 1994. Statistics. 5th ed. New York: Holt, Rinehart and Winston. https://www.amazon.com/Statistics-William-Hays/dp/0030744679.

Islam, Mohammad Rafiqul. 2018. “Sample Size and Its Role in Central Limit Theorem (CLT).” International Journal of Physics and Mathematics 1 (1): 37–46. https://doi.org/10.31295/pm.v1n1.42.

Kerns, G J. 2011. Introduction to Probability and Statistics Using R. 1st ed.

Kwak, Sang Gyu, and Jong Hae Kim. 2017. “Cornerstone of Modern Statistics.” Korean Journal of Anesthesiology 70 (2): 144–56.

Mwiti, Mbuba Morris, Samson W. Wanyonyi, and Davis Mwenda Marangu. 2019. “Central Limit Theorem and Its Applications in Determining Shoe Sizes of University Students.” Asian Journal of Probability and Statistics 3 (1): 1–9. https://doi.org/10.9734/ajpas/2019/v3i130082.

Rahayu, Widyanti, and Siti Rohmah Rohimah. 2015. “Meningkatkan Keterampilan Menggunakan Software R Sebagai Solusi Untuk Meningkatkan Inovasi Pembelajaran Bagi Guru-Guru Matematika Sma Dan Smk Di Jakarta Timur.” Sarwahita 12 (2): 134–40. https://doi.org/10.21009/sarwahita.122.10.

Sarvina, Yeli. 2017. “PEMANFAATAN SOFTWARE OPEN SOURCE ‘ R ’ UNTUK PENELITIAN AGROKLIMAT ‘ R ’ OPEN SOURCE SOFTWARE FOR AGROCLIMATE RESEARCH.” Informatika Pertanian 26 (1): 23–30.

Sihombing, Rika Elizabet, Dewi Rachmatin, and Jarnawi Afgani Dahlan. 2019. “Program Aplikasi Bahasa R Untuk Pengelompokan Objek Menggunakan Metode K-Medoids Clustering.” Jurnal EurekaMatika 7 (1): 58–79.

Sungkono, Joko, and Kriswianti Nugrahaningsih. 2020. “Pembelajaran Teori Probabilitas Menggunakan R.” Absis: Mathematics Education Journal 2 (1): 1. https://doi.org/10.32585/absis.v2i1.858.

Taylor, Marshall A. 2018. “Simulating the Central Limit Theorem.” Stata Journal 18 (2): 345–56. https://doi.org/10.1177/1536867x1801800203.

Venables, W. N., and D. M. Smith. 2021. “Notes on R: A Programming Environment for Data Analysis and Graphics Version 4.1.2.” In An Introduction to R. https://doi.org/10.4135/9781473920446.n12.

Wulandari, Andhika Ayu, Annisa Prima Exacta, and Joko Sungkono. 2021. “Efektivitas Simulasi ‘R’ Dalam Pembelajaran Distribusi Peluang Variabel Random.” AKSIOMA: Jurnal Program Studi Pendidikan Matematika 10 (2): 692–700. https://doi.org/https://doi.org/10.24127/ajpm.v10i2.3380.

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Published

2022-06-30

How to Cite

Sungkono, J., & Wulandari, A. A. (2022). Pembelajaran Teorema Limit Pusat Melalui Simulasi. Absis: Mathematics Education Journal, 4(2), 69–76. https://doi.org/10.32585/absis.v4i2.2520