What Is Variance? Definition And How To Calculate It
By Indeed Editorial Team
Updated September 27, 2021 | Published February 4, 2020
Updated September 27, 2021
Published February 4, 2020
The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.
Variance is a measure of the distance of each variable from the average value or mean in its data set. It is used to calculate deviation within the set and it’s a valuable tool for investors and finance professionals. In this article, we define variance, how to calculate it and the advantages and disadvantages of using variance.
What is variance?
Variance is a calculation that considers random variables in terms of their relationship to the mean of its data set. Variance can be used to determine how far each variable is from the mean and, in turn, how far each variable is from one another. It is also used in statistical inferences, hypothesis testing, Monte Carlo methods (random sampling) and goodness-of-fit analyses.
How is variance used?
Variance is used in investing to determine the individual performance of the separate parts of an investment portfolio. This helps asset managers and investors improve their investment performance.
Other professionals who might use variance are scientists, statisticians, mathematicians, data analysts and anyone responsible for identifying risk or determining information about the population of an experiment or sample.
In some cases, variance and standard deviation can be used interchangeably. Someone might choose standard deviation over variance because it's a smaller number, which in some cases might be easier to work with and is less likely to be impacted by skewing. To find the standard deviation, simply take the square root of the variance. With this number, you can draw the same kinds of inferences you would if you were using variance, but with smaller computations.
Related: How To Perform Risk Analysis
How to calculate variance
To calculate variance, you need to square each deviation of a given variable (X) and the mean.
In a sample set of data, you would subtract every value from the mean individually, then square the value, like this: (μ - X)². Then, you would add all the squared deviations and divide them by the total number of values to reach an average. This number is the variance.
To find the standard deviation, you could simply take the square root of the variance.
The formula for variance is as follows:
Var(X) = E (x - μ)**² / N**
The formula shows that the variance of X (Var[X]) is equal to the average of the square of X minus the square of its mean. And you can solve it by dividing it across the amount of numbers in a set, or N.
How to use variance data
In a risk assessment, investors use the mean to determine variability that could equate to risk within a portfolio. This is often used when considering a new purchase to decide whether the investment is worth the risk. The variance helps risk analysts determine a measure of uncertainty, which without variance and the standard deviation is difficult to quantify.
While uncertainty isn't expressly measurable, variance and standard deviation allow analysts to determine the estimated impact a particular stock could have on a portfolio.
In statistics, the variance is used to determine how well the mean represents an entire set of data.
For instance, the higher the variance, the more range exists within the set. Data scientists can use that information to infer that the mean may not reflect the set as well as it would if the set had a lower variance. Researchers might look for variance between test groups to determine if they are similar enough to test a hypothesis successfully.
Related: Financial Analyst Resume Samples
What are the advantages of using variance?
The biggest advantage to using variance is to gain information about a set of data. Whether you are an investor looking to mitigate risk or a statistician who needs to understand the spread of a sample, the variance is information that people can use to draw quick inferences.
It's faster to use a variance than to plot each number on a spread and determine the approximate distance from the mean and each variable. This measure allows people who use statistics to make important estimations with a relatively quick calculation that provides information about the range of a sample.
Variance treats all numbers in a set the same, regardless of whether they are positive or negative, which is another advantage to using this formula.
Related: Types of Graphs and Charts
What are the disadvantages of using variance?
One disadvantage of using variance is that larger outlying values in the set can cause some skewing of data, so it isn't necessarily a calculation that offers perfect accuracy. That's because, once squared, outliers on either side of the population can have a significant weight associated with them depending on the values in the rest of the sample.
This is exacerbated by the fact that some researchers prefer to work with smaller numbers, so they might prefer to work in standard deviations, which takes the square root of the variance and is less likely to skew heavily toward high numbers. Variance can also be difficult to interpret, which is another reason why its square root might be preferable.
An example of variance
In this investment example, let's say your stock returns are 10% in a first-year investment, 20% in year two and 15% in the third year. The average return is 15%.
Now, let's take the difference of each return and the average return, which looks like this:
|Year One||10% - 15% = -5%||-5%² = 25%|
|Year Two||20% - 15% = 5%||5%² = 25%|
|Year Three||15% - 15% = 0%||0%² = 0|
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