Variance is a statistical measurement of the spread between numbers in a data set. It is a measure of how far a set of numbers is spread out from their average value. More specifically, variance measures how far each number in the set is from the mean (average), and thus from every other number in the set. It is calculated by taking the differences between each number in the data set and the mean, then squaring the differences to make them positive, and finally dividing the sum of the squares by the number of values in the data set. The variance is expressed in much larger units than the original values of the data set, making it harder to interpret intuitively. The square root of the variance is the standard deviation, which is often preferred as a main measure of variability because it is expressed in the same units as the original values of the data set. However, the variance is more informative about variability than the standard deviation, and it is used in making statistical inferences. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling.