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Variance analysis can be carried out for both costs and revenues. Variance analysis is usually associated with explaining the difference (or variance) between actual costs and the standard costs allowed for the good output. For example, the difference in materials costs can be divided into a materials price variance and a materials usage variance.
In estimating the mean of uncorrelated, identically distributed variables we can take advantage of the fact that the variance of the sum is the sum of the variances.In this case efficiency can be defined as the square of the coefficient of variation, i.e., [13]
The company produced 2000 units of product A during the month. The labor efficiency variance is (4500 - 5000) x $14 = $7000, where 5000 hours = 2.5 hours x 2000 units of output. This variance is favorable since the actual hours used are less than the standard hours allowed.
A pre-determined overhead rate is normally the term when using a single, plant-wide base to calculate and apply overhead. Overhead is then applied by multiplying the pre-determined overhead rate by the actual driver units. Any difference between applied overhead and the amount of overhead actually incurred is called over- or under-applied overhead.
This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
Variance is invariant with respect to changes in a location parameter. That is, if a constant is added to all values of the variable, the variance is unchanged: (+) = (). If all values are scaled by a constant, the variance is scaled by the square of that constant:
Variable costs as a percentage of sales are equal to 100% minus the contribution margin ratio. Thus, in the above income statement, the variable costs are 60% (100% - 40%) of sales, or $648,000 ($1,080,000 X 60%).
The variance of randomly generated points within a unit square can be reduced through a stratification process. In mathematics , more specifically in the theory of Monte Carlo methods , variance reduction is a procedure used to increase the precision of the estimates obtained for a given simulation or computational effort. [ 1 ]