Gaussverdeling

Gaussverdeling, also known as the normal distribution or bell curve, is a fundamental probability distribution in statistics. It is characterized by its symmetric, bell-shaped curve, which is centered around its mean. The distribution is defined by two parameters: the mean (μ) and the standard deviation (σ). The mean determines the location of the peak of the curve, while the standard deviation determines the spread or width of the curve. A smaller standard deviation results in a taller, narrower curve, indicating that the data points are clustered closely around the mean. Conversely, a larger standard deviation leads to a shorter, wider curve, signifying greater variability in the data.

The Gaussverdeling is widely used because it describes many natural phenomena, such as the distribution of heights, weights, and measurement errors. It also plays a crucial role in statistical inference, particularly in hypothesis testing and confidence interval estimation, due to its relationship with the Central Limit Theorem. This theorem states that the distribution of sample means will approach a normal distribution as the sample size increases, regardless of the shape of the underlying population distribution. The area under the curve of a Gaussverdeling represents probability. For instance, approximately 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and nearly 99.7% within three standard deviations. This predictable pattern makes the Gaussverdeling a powerful tool for understanding and analyzing data.