Calculate standard deviation and variance that measure data dispersion. Essential tool for statistical analysis, quality control, and data science.
Standard deviation measures how far data points are from the mean. Small standard deviation means data is clustered around the mean; large means data is spread out. Used for analyzing test scores, quality control, stock volatility, etc.
Variance is the average of squared differences from the mean. Standard deviation is the square root of variance, using the same unit as original data for easier interpretation. For example, if height variance is 100cm², standard deviation is 10cm.
Population standard deviation covers all data, dividing by n. Sample standard deviation estimates population from partial data, dividing by n-1 (Bessel's correction). Most real-world situations use sample standard deviation.
In normal distribution, about 68% of data falls within ±1 standard deviation from mean, 95% within ±2, and 99.7% within ±3. This rule is used in quality control (Six Sigma), confidence intervals, outlier detection, etc.
Coefficient of Variation is standard deviation divided by mean, useful for comparing dispersion of data with different units. CV = (Std Dev/Mean) × 100%. For example, directly compare variability of height and weight.
Measuring volatility (risk) in stock investing, verifying product quality consistency in manufacturing, analyzing student grade distribution in education, predicting temperature fluctuations in meteorology, evaluating clinical trial results in medicine.