Calculate the sample and population variance of a data set with our online calculator. Easily find statistical dispersion. Use a period as the decimal separator.
Sample Variance (s2)
Population Variance (σ2)
Variance is a statistical measure that quantifies the dispersion or variability of a data set with respect to its statistical mean. Essentially, variance indicates how far individual values are from the average of the data set.
In simpler terms, if all data in a set are very similar to each other, the variance will be low, indicating little dispersion. Conversely, if the data vary significantly, the variance will be high, signaling greater dispersion.
There are two main types of variance used in statistics to measure data dispersion: sample variance and population variance. Each applies in different contexts depending on whether you are working with a sample or a complete population.
Sample variance is calculated when only a sample of the population is available. It is used to estimate the population variance and is calculated by dividing the sum of the squared differences between each data point and the sample mean by the number of data points in the sample minus one (n-1). This adjustment, known as Bessel’s correction, corrects the bias in estimating the population variance.
Population variance is calculated when data for the entire population is available. It is obtained by dividing the sum of the squared differences between each data point and the population mean by the total number of data points in the population (N). This formula does not require correction, as it is based on all available data.
To calculate variance, first you need to find the statistical mean of your data. Then, subtract the calculated mean from each individual value, square the result, and sum these squares. If you are working with a sample, divide the sum of the squares by the total number of data points minus one (n-1) to obtain the sample variance. If you are working with the entire population, divide by the total number of data points (N) to obtain the population variance.
Where:
Where:
The statistical mean x is calculated by summing all values in the sample and dividing by the total number of data points.
Where:
Variance helps you understand how consistent or variable the data in a set are. Imagine you are evaluating the grades of a group of students on an exam. If the variance is low, it means that most students received similar grades, suggesting that the exam was fair to everyone. Conversely, a high variance indicates that the grades are very dispersed, which could signal that some students found the exam much harder than others.
In summary, variance allows you to see how data cluster around the mean and whether there is a lot or little variability in the set.