Penerapan Distribusi Normal Dalam Pengukuran Tinggi Badan Mahasiswa FMIPA Universitas Negeri Medan 2024

Abstract

This study explores the application of the normal distribution in analyzing the height data of Mathematics Education students at FMIPA Universitas Negeri Medan in 2024. Employing a quantitative descriptive-analytic methodology, the research involved collecting primary data from 10 randomly selected students through a questionnaire-based survey. Descriptive statistical analysis revealed a mean height of 161.4 cm with a standard deviation of 8.79 cm. The median height was found to be 164 cm, while the mode was 150 cm, indicating a slightly skewed distribution. To assess the suitability of the normal distribution model, the Shapiro-Wilk test was applied, resulting in a W value of 0.921 and a p-value of 0.361, which exceeds the 0.05 significance level. This confirms that the sample data follow a normal distribution pattern. The findings were further supported through visual representation using histograms and analysis based on the empirical rule, which showed that approximately 68% of the students' heights fall within one standard deviation of the mean (152.81–169.99 cm). Additionally, probability calculations demonstrated that the likelihood of a student being 160 cm tall or shorter is approximately 43.64%. These results validate the effectiveness of the normal distribution as a tool for analyzing biological or physical characteristics, even in small sample sizes. However, the study acknowledges its limitation in terms of sample size and suggests that future research involve larger and more diverse populations to enhance generalizability. The study highlights the relevance of normal distribution in statistical modeling, particularly for educational and health-related data interpretation and decision-making processes.