Variance is a statistical measure of the spread between numbers in a data set. It measures how far each number in the set is from the mean (average) and from every other number in the set. Variance is often depicted by the symbol σ². It is used by both analysts and traders to determine volatility and market security. The square root of the variance is the standard deviation, which helps determine the consistency of an investment’s returns over a period of time.

Statisticians use variance to see how individual numbers relate to each other within a data set, rather than using broader mathematical techniques such as arranging numbers into quartiles. The advantage of variance is that it treats all deviations from the mean as the same regardless of their direction. The squared deviations cannot sum to zero and give the appearance of no variability.

To calculate variance, statisticians take the differences between each number in the data set and the mean, then square the differences to make them positive, and finally divide the sum of the squares by the number of values in the data set. The formula for variance is σ² = N∑i=1n(xi−x)², where xi is each value in the data set, x is the mean of all values in the data set, and N is the number of values in the data set.

Variance is expressed in much larger units than those of a typical value of a data set, making it harder to interpret the variance number intuitively. That’s why standard deviation is often preferred as a main measure of variability. However, the variance is more informative about variability than the standard deviation, and it’s used in making statistical inferences.

In summary, variance is a measure of how data points differ from the mean, and it is calculated by taking the average of squared deviations from the mean. It is used to determine volatility and market security, and it is often depicted by the symbol σ². The squared deviations cannot sum to zero and give the appearance of no variability.