Variancë

Variancë is a statistical measure used to quantify the dispersion or spread of a set of data points around their mean. It is a fundamental concept in probability theory and statistics, providing insight into how much individual values in a dataset deviate from the average. The term originates from the Latin *varians*, meaning "changing or varying," reflecting its role in assessing variability within data.

Variancë is calculated by taking the average of the squared differences between each data point and the mean of the dataset. For a population variance, denoted as σ², the formula is:

σ² = (Σ(xi - μ)²) / N

where xi represents each data point, μ is the population mean, and N is the total number of observations. In sample variance, denoted as s², the denominator is adjusted to N - 1 to account for bias, ensuring a more reliable estimate of the population variance.

Variancë is always non-negative, with a value of zero indicating that all data points are identical to the mean. Higher values suggest greater dispersion among the data. It is closely related to standard deviation, which is simply the square root of variance and provides a measure in the same units as the original data.

Variancë is widely used in hypothesis testing, regression analysis, and other statistical methods to assess consistency, reliability, and predictability in datasets. It plays a crucial role in fields such as finance, engineering, and social sciences, where understanding variability is essential for informed decision-making.