A variance has several meanings in business. In an accounting sense, a variance is the difference between an actual amount and a pre-determined standard amount. In a statistical sense, a variance is a measure of the amount of spread in a distribution. It is computed as the average squared deviation of each number from its mean.
In accounting, a variance could be a cost variance, where actual costs may be different from the estimated standards for costs. Variances can be favorable or unfavorable. A variance from standard cost is considered favorable if the actual cost is less than the standard cost, and it is considered unfavorable if the actual cost is more than the standard cost. It is also possible to break down the cost variance into the factors that may have caused it to occur—such as a quantity variance, or the difference between the actual quantity and the standard quantity; and a price variance, or the difference between the actual price and the standard price.
When a variance occurs, like the cost variance in this example, top management should examine the circumstances to determine the factors that created it. By doing so, management should be able to identify who or what was responsible for the variance and take steps to correct the problem. For example, assume that the standard material cost for producing 1,000 units of a product is $8,000, but that materials costing $10,000 were actually used. The $2,000 unfavorable variance may have resulted from paying a price for the material that was higher than the standard price. Alternatively, the process may have used a greater quantity of material than standard. Or, there may have been some combination of these factors.
The purchasing department is usually responsible for the price paid for materials. Therefore, if the variance was caused by a price higher than standard, responsibility for explaining the problem rests with the purchasing manager. On the other hand, the production department is usually responsible for the amount of material used. Thus, the production department manager is responsible for explaining the problem if the process used more than the standard amount of materials. However, the production department may have used more than the standard amount of material because its quality did not meet specifications, with the result that more waste was created. Then the purchasing manager is responsible for explaining why the inferior materials were acquired. On the other hand, the production manager is responsible for explaining what happened if the analysis shows that the waste was caused by inefficiencies.
Thus variances—like the cost variance in the example above—trigger questions to be answered within the organization. These questions call for answers that, in turn, should lead to changes designed to correct the problem and minimize or eliminate the variances for the next reporting period. A performance report may identify the existence of the problem, but it can do no more than point the direction for further investigation of what can be done to improve future results. Other common variances in accounting include overhead rate and usage variances.
In statistics, a variance is also called the mean squared error. The variance is one of several measures that statisticians use to characterize the dispersion among the measures in a given population. To calculate the variance, it is necessary to first calculate the mean or average of the scores. The next step is to measure the amount that each individual score deviates or is different from the mean. Finally, you square that deviation by multiplying the number by itself. Numerically the variance equals the average of the squared deviations from the mean.