Variance: Definition, Formulas & Calculations


Consequently, variance is always greater than or equal to zero. It is almost always a positive value because only datasets containing one repeated value (e.g., all values equal 15) have a value of zero. Here’s an example of how to calculate the variance using the sample formula. The numbers in parentheses correspond to table columns. Subtracting the mean from each number in the data set and then squaring the result. The results are squared to make the negatives positive.


Variance is a measure of dispersion of data points from the mean. Low variance indicates that data points are generally similar and do not vary widely from the mean.

Calculating the Variance

This means that one estimates the mean and variance from a limited set of observations by using an estimator equation. The estimator is a function of the sample of n observations drawn without observational bias from the whole population of potential observations. In this example that sample would be the set of actual measurements of yesterday’s rainfall from available rain gauges within the geography of interest. To see how, consider that a theoretical probability distribution can be used as a generator of hypothetical observations.

A goodness-of-fit test helps you see if your sample data is accurate or somehow skewed. Discover how the popular chi-square goodness-of-fit test works.

Properties & Relations  (

And standard deviation calculator, which shows you the step-by-step calculations for your individual data set. is essentially the degree of spread in a data set about the mean value of that data. It shows the amount of variation that exists among the data points.

What is variance and deviation?

The variance measures the average degree to which each point differs from the mean. While standard deviation is the square root of the variance, variance is the average of all data points within a group. The two concepts are useful and significant for traders, who use them to measure market volatility.

Watch the video for an example of how to find the sample Variance. Three-Sigma Limits is a statistical calculation that refers to data within three standard deviations from a mean. Here’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 differences between each return and the average are 5%, 15%, and −20% for each consecutive year.

Discrete random variable variance calculator

So to summarize, if \( X \) has a normal distribution, then its standard score \( Z \) has the standard normal distribution. Is there any specific reason behind having n-1 as denominator for calculating sample variance? I couldn’t get the logic “to counteract a bias where samples tend to underestimate the population value”. When there is no variability in a sample, all values are the same, and the variance equals zero. As the data values spread out further, variability increases.

To find the variance, take a data point, subtract the population mean, and square that difference. Then, sum all of those squared values and divide by the number of observations. Use the population form of the equation when you have values for all members of the group of interest. In this case, you are not using the sample to estimate the population. Instead, you have measured all people or items and need the variance for that specific group.

Data Analysis

Then var(A,0,) returns a 1-by-1-by-3 array whose elements are the variances computed over each page of A. Vector made up of nonnegative scalar weights corresponding to the dimension of A along which the variance is calculated. Create a vector and compute its variance, excluding NaN values. Create a 3-D array and compute the variance over each page of data . Create a matrix and compute its variance along the first dimension.

  • Young people’s reactions to world events are often at variance with those of their parents.
  • The result is a positive semi-definite square matrix, commonly referred to as the variance-covariance matrix .
  • Under most codes governing variances, approval of the variance must not result in a public health or safety hazard and must not grant special privilege to the property owner.
  • Performing the estimation for each period, we obtained estimates for the parameters and variances.
  • It gives you a sense of how spread apart the data is from the mean.

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