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Learn how to calculate and interpret the sample mean and covariance, statistics computed from a sample of data on one or more random variables. The sample mean is the average value of a sample, and the sample covariance is a matrix of pairwise correlations between variables.
Learn how to calculate the standard deviation of a random variable, a sample, or a population using different formulas and examples. The standard deviation measures the amount of variation of a data set around its mean.
Welford's algorithm is a numerically stable way to compute the variance of a sequence in a single pass, using the sum of squares of differences from the mean. Learn the formula, implementation, and analysis of this algorithm, as well as its variations and alternatives.
Variance is a measure of how far a set of numbers is spread out from their average value. It is the expected value of the squared deviation from the mean of a random variable, and it has various properties and applications in probability and statistics.
In statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical dispersion) of a population of values, in such a way that the expected value of the calculation equals the true value.
Learn the definition and examples of bias and unbiasedness of an estimator in statistics. Compare different types of bias and unbiasedness, such as mean-unbiasedness and median-unbiasedness, and how they affect the performance of estimators.
Bessel's correction is the use of n − 1 instead of n in the formula for the sample variance and standard deviation. It corrects the bias in the estimation of the population variance, but not the standard deviation.
Learn about the t distribution, a continuous probability distribution that generalizes the normal distribution and is used in statistical tests and confidence intervals. Find out its history, definition, properties, moments, and special cases.