What's the difference between standard deviation and standard error, and why is this important when using variance?

Standard deviation measures the spread of data points *within* a single sample. Standard error measures the spread of sample statistics (like the mean) *across multiple samples*. Variance is a component in calculating both. Using variance to calculate standard deviation describes the data itself. Using variance (through standard error) to describe the reliability of a sample statistic is crucial for inferential statistics and hypothesis testing – it tells you how much your sample result might differ from the true population value.