What is variance in statistics

More specifically, variance measures how far each number in the set is from the mean and thus from every other number in the set. It is used by both analysts and traders to determine volatility and market security. In 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, 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.

Variance is calculated by using the following formula:. A large variance indicates that numbers in the set are far from the mean and far from each other. A small variance, on the other hand, indicates the opposite. A variance value of zero, though, indicates that all values within a set of numbers are identical. A variance cannot be negative. Variance is an important metric in the investment world. Variability is volatility, and volatility is a measure of risk.

It helps assess the risk that investors assume when they buy a specific asset and helps them determine whether the investment will be profitable. But how is this done? Investors can analyze the variance of the returns among assets in a portfolio to achieve the best asset allocation.

In financial terms , the variance equation is a formula for comparing the performance of the elements of a portfolio against each other and against the mean. You can also use the formula above to calculate the variance in areas other than investments and trading, with some slight alterations. 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 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 set. 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. 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. Now, let's take the difference of each return and the average return, which looks like this:. Find jobs. Company reviews. Find salaries. Upload your resume. Sign in. Career Development. What is variance? How is variance used? How to calculate variance. How to use variance data. What are the advantages of using variance? What are the disadvantages of using variance? An example of variance.

What Is a Content Hub? Related View More arrow right. So that's five data points. And I'm going to divide by 5. And I get 6. So the population mean, for years of experience at my organization, is 6. Well, that's, I guess, interesting. But now I want to ask another question. I want to get some measure of how much spread there is around that mean. Or how much do the data points vary around that mean.

And obviously, I can give someone all the data points. But instead, I actually want to come up with a parameter that somehow represents how much all of these things, on average, are varying from this number right here.

Or maybe I will call that thing the variance. And so, what I do-- so the variance-- and I will do-- and this is a population variance that I'm talking about, just to be clear, it's a parameter. The population variance I'm going to denote with the Greek letter sigma, lowercase sigma-- this is capital sigma-- lowercase sigma squared. And I'm going to say, well, I'm going to take the distance from each of these points to the mean. And just so I get a positive value, I'm going to square it.

And then, I'm going to divide by the number of data points that I have. So essentially, I'm going to find the average squared distance. Now that might sound very complicated, but let's actually work it out. So I'll take my first data point and I will subtract our mean from it.

So this is going to give me a negative number. But if I square it, it's going to be positive. So it's, essentially, going to be the squared distance between 1 and my mean. And then, to that, I'm going to add the squared distance between 3 and my mean. And to that, I'm going to add the squared distance between 5 and my mean.

And since I'm squaring, it doesn't matter if I do 5 minus 6, or 6 minus 5. When I square it, I'm going to get a positive result regardless.

And then, to that I'm going to add the squared distance between 7 and my mean. So 7 minus 6 squared. All of this, this is my population mean that I'm finding the difference between. And then, finally, the squared difference between 14 and my mean. And then, I'm going to find, essentially, the mean of these squared distances. So I have five squared distances right over here.

So let me divide by 5. So what will I get when I make this calculation, right over here? Well, let's figure this out.