4.6 : Variance

The variance is a statistic estimating the variability of the dataset values from the mean. It is numerically equal to the square of the standard deviation of a dataset.

The variance is a valuable statistical tool used in the analysis of variance, estimation of risk, or volatility in financial markets.

The sample variance is denoted as the square of the sample standard deviation s, while the population variance is expressed as the square of the population standard deviation sigma.

Imagine if one were to estimate sample variance of weight of polar bears in different Arctic regions. On dividing the population into random samples and calculating the sample variances, one observes that the values center around the constant population variance value. Thus, the sample variance is an impartial estimator of the population variance.

The major disadvantage of variance is that its units vastly differ from the dataset units. For instance, the units of variance of rainfall in a year will be millimeters squared, which is unhelpful. Therefore, in most analyses, standard deviation is preferred to variance.