Variance is a statistical measure of how closely or widely the individual points in a set of data are dispersed. In simple terms, it measures the average difference between an individual results and the overall average result. It can help put data into context and identify possible errors, but in its raw form can be difficult to comprehend in a meaningful way.
To calculate variance, add up the individual figures (data points), then find the mean average. For each individual data point, you then find the difference between the data point and the mean average, then square this difference. Repeat this process for each data point, then calculate the mean average of all the squared differences.
Finding the variance in a data set can give a useful insight into the group covered by the data set. For example, if the data covers ages of television viewers in a particular region, a low variance means station controllers can safely concentrate on airing shows aimed at a particular age group. A high variance would mean such a strategy would be unlikely to work.
In many types of data, although the actual figures may change over time (for example, a country's population become heavier), the variation will often remain relatively steady. This can help statistical researchers verify results. If somebody looking at average weight finds the result has increased by 10 percent compared with a similar study a decade before, this doesn't give the researcher any insight into the reliability of the data. However, if the researcher finds the variation in the new research is much higher than the variation in the previous study, it is an indication that one of the two studies had a collation or calculation error. The more studies with variation figures available, the easier it is to identify which may have had the errors.
The way variance is calculated means you can't readily compare the variance figure to individual data points. This is because of the squaring action during the calculation. To allow a meaningful comparison, you must go on to calculate the standard deviation, which is simply the square root of the variable. For example, if you calculate the variance in the height of a group of schoolchildren, the result may be 36 cm (14 inches) but this doesn't directly compare to a child's height. If you use the standard deviation, 6 cm (2.4 inches), you are using directly comparable units.