# Updating mean and variance estimates an improved method Having accurate project estimates and a robust project budget is necessary to deliver within the project budget.

Both Estimating Costs and Determining Budget are project planning processes.

If the project is delayed or over-budget, you can use TCPI to determine the project performance required to complete the project as budgeted or estimated. Variance analysis is the comparison of expected project performance to the actual cost performance.

This analysis helps you understand the causes of variance, if any.

It is often useful to be able to compute the variance in a single pass, inspecting each value only once; for example, when the data are being collected without enough storage to keep all the values, or when costs of memory access dominate those of computation.

The variance is invariant with respect to changes in a location parameter, a property which can be used to avoid the catastrophic cancellation in this formula.

are small then there are no problems with the sum of its squares, on the contrary, if they are large it necessarily means that the variance is large as well.

A better quantity for updating is the sum of squares of differences from the current mean, This algorithm is much less prone to loss of precision due to catastrophic cancellation, but might not be as efficient because of the division operation inside the loop.

For a particularly robust two-pass algorithm for computing the variance, one can first compute and subtract an estimate of the mean, and then use this algorithm on the residuals.