Variance and Standard Deviation

Learn how variance and standard deviation quantify the spread of probability distributions through this 13-minute educational video. Explore the fundamental definition of variance as the expected value of the squared deviation from the mean, then derive an alternative computational formula that simplifies calculations. Work through a detailed example calculating the variance of a Gaussian distribution and complete an exercise proving that variance is always non-negative. Discover how variance behaves when dealing with independent random variables and their sums. Master these essential statistical concepts that form the foundation for understanding data variability and distribution characteristics in probability theory and statistical analysis.