what is variance 
variance is a statistical measurement of the spread between numbers in a data set 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 variance is often depicted by this symbol 2 it is used by both analysts and traders to determine volatility and market security the square root of the variance is the standard deviation sd or which helps determine the consistency of an investment s returns over a period of time investopedia alex dos diazunderstanding variancein statistics variance measures variability from the average or mean it is calculated by taking the differences between each number in the data set and the mean squaring the differences to make them positive and then dividing the sum of the squares by the number of values in the data set software like excel can make this calculation easier variance is calculated by using the following formula 2 i 1 n x i x 2 n where x i each value in the data set x mean of all values in the data set n number of values in the data set begin aligned sigma 2 frac sum i 1 n big x i overline x big 2 n textbf where x i text each value in the data set overline x text mean of all values in the data set n text number of values in the data set end aligned 2 n i 1n xi x 2 where xi each value in the data setx mean of all values in the data setn number of values in the data set you can also use the formula above to calculate the variance in areas other than investments and trading with some slight alterations for instance when calculating a sample variance to estimate a population variance the denominator of the variance equation becomes n 1 so that the estimation is unbiased and does not underestimate the population variance advantages and disadvantages of variancestatisticians 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 at all in the data one drawback to variance though is that it gives added weight to outliers these are the numbers far from the mean squaring these numbers can skew the data another pitfall of using variance is that it is not easily interpreted users often employ it primarily to take the square root of its value which indicates the standard deviation of the data as noted above investors can use standard deviation to assess how consistent returns are over time in some cases risk or volatility may be expressed as a standard deviation rather than a variance because the former is often more easily interpreted example of variance in financehere s a hypothetical example to demonstrate how variance works let s say returns for stock in company abc are 10 in year 1 20 in year 2 and 15 in year 3 the average of these three returns is 5 the differences between each return and the average are 5 15 and 20 for each consecutive year squaring these deviations yields 0 25 2 25 and 4 00 respectively if we add these squared deviations we get a total of 6 5 when you divide the sum of 6 5 by one less the number of returns in the data set as this is a sample 2 3 1 it gives us a variance of 3 25 0 0325 taking the square root of the variance yields a standard deviation of 18 0 0325 0 180 for the returns 