Standard Deviation vs. Variance

Two statistical measures that are often quite confusing for many people are standard deviation and variance. Both are measures of the distribution of data, representing the amount of variation there is from the average, or to the range the values normally differ from the average, which is also called the mean. If the variance or standard deviation has a value of zero, all the values are identical.

Variance is the mean or average of the squares of the deviations or differences in the values from the mean. On the other hand, standard deviation is the square root of that variance. The two are closely related, but standard deviation is used to identify the outliers in the data.

There is one similarity between the two values. The standard deviation and the variance values will always be non-negative.

The mathematical formula for a standard deviation is the square root of the variance. On the other hand, the variance's formula is the average of the squares of deviations of each value from the mean in a sample. The deviations are squared to prevent negative values from canceling out the positive values.

The symbol for standard deviation is the Greek letter sigma: σ. There is no dedicated symbol for variance, and it is expressed in the same unit as the values themselves.

In the real world, standard deviation is used with population sampling data and identifying outliers. For variance, it used with statistical formulas and in the world of finance.

To understand the difference between the values can be done by reviewing an example. Using the following values: 5, 8, 4, 7, 6. The mean or average is equal to: 6. Finding the variance, one must subtract the mean from each value, squaring each result: 5 - 6 = -12, 8 - 6 = 22, etc. Next, add the squares and find the mean or average: 1 + 4 + 4 + 1 + 0 = 10/5 = 2. The variance of the data is 2.

To find the standard deviation, calculate the square root of the variance: √2 = standard deviation.

The variance of the set of data is an arbitrary number (2) relative to the original measurements of the data set. This makes it difficult to visualize and apply in the real world, but useful in finance and statistical formulas.

The standard deviation (√2 = 1.4) is expressed in the original units of the data set. This value is more natural and closer to the values of the original data set and most often used to analyze demographics or population samples.

In summary, standard deviation cannot be calculated without first finding the variance of a set of data, and variance is then used to discover the standard deviation. The steps to find each figure are similar, but standard deviation is used more often in the real world, such as for populations, versus variance, which is most useful for other statistical formulas and the finance world.