Variance

Variance asks how far values lie from their mean, squares each distance, and aggregates the results. Squaring prevents positive and negative deviations from canceling and gives large deviations more influence.

For a complete population of size (N):

[ \sigma^2=\frac{\sum (x_i-\mu)^2}{N}. ]

For a sample used to estimate population spread, this module uses:

[ s^2=\frac{\sum (x_i-\bar{x})^2}{n-1}. ]

The n - 1 denominator accounts for the degree of freedom used when the sample mean is estimated from the same observations. Statistical software often exposes this denominator choice through a setting named ddof (delta degrees of freedom); an undocumented default is not a declared convention.

Squared units are both feature and burden

If settlement time is measured in days, variance is measured in squared days. That makes it useful algebraically but awkward to explain directly. Standard deviation takes the square root and returns to days.

Variance is sensitive to extreme values because the deviations are squared. That sensitivity may reveal consequential tail behavior, or it may make the summary unstable for the purpose. Inspect the distribution before interpreting the number.