Variance is a statistical measure that quantifies the dispersion of a set of data points around their mean, providing insight into the degree of spread in the dataset. A higher variance indicates that the data points are more spread out from the mean, while a lower variance suggests they are closer to the mean.
The mean, often referred to as the average, is a measure of central tendency that is calculated by summing all the values in a dataset and dividing by the number of values. It provides a useful summary of the data but can be heavily influenced by outliers, making it less representative in skewed distributions.
Covariance is a statistical measure that indicates the extent to which two random variables change together, reflecting the direction of their linear relationship. A positive covariance indicates that the variables tend to increase or decrease together, while a negative covariance suggests that one variable increases as the other decreases.
Sample variance is a statistical measure that quantifies the dispersion or spread of a set of data points in a sample. It provides insight into how much individual data points deviate from the sample mean, serving as a crucial component for inferential statistics and hypothesis testing.
Population standard deviation is a measure of the dispersion or spread of a set of data points in a population, indicating how much individual data points deviate from the mean of the population. It is calculated as the square root of the variance and provides insight into the variability of the entire population rather than just a sample.
A zero-centered distribution is a probability distribution where the mean is zero, often used in statistical models to simplify calculations and ensure symmetry around the origin. This characteristic is particularly useful in machine learning and finance, where it helps in normalizing data and reducing bias in predictive models.
Gaussian distributions, also known as normal distributions, are fundamental in statistics due to their symmetric, bell-shaped curve characterized by mean and standard deviation. They are central to the Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the original distribution's shape.
A Cumulative Gaussian Distribution, also known as the cumulative distribution function (CDF) of a normal distribution, represents the probability that a normally distributed random variable is less than or equal to a given value. It is a non-decreasing, continuous function ranging from 0 to 1, providing a complete description of the distribution's probability structure over its domain.