Enter a comma-separated data set and choose sample or population to get variance, standard deviation, mean, and count instantly.
Estimates only.
Variance measures how far each value in a data set is from the mean. A low variance means values cluster near the mean; a high variance means they are spread out. Standard deviation is simply the square root of variance, expressed in the same units as the original data.
For the default set (4, 8, 6, 5, 3, 7): mean = 5.5; sum of squared deviations = 17.5; sample variance = 17.5 / 5 = 3.5; standard deviation = sqrt(3.5) = 1.871.
1. Find the mean: add all values and divide by the count. 2. Subtract the mean from each value and square each result. 3. Sum all those squared differences. 4. For sample variance, divide by n minus 1. For population variance, divide by n. For example, the sample variance of 4, 8, 6, 5, 3, 7 is: mean = 5.5; sum of squared deviations = 17.5; variance = 17.5 / 5 = 3.5.
The range (maximum minus minimum) is the simplest measure of spread, but it only uses two data points. For a more robust measure, variance uses every data point. The interquartile range (IQR), which is the 75th percentile minus the 25th percentile, is another simple spread measure that is resistant to outliers.
A variance calculator takes a data set, computes the mean, then finds the average squared distance each data point sits from that mean. This tool supports both sample variance (divides by n minus 1) and population variance (divides by n), and also returns the standard deviation and mean.
Sample variance: s^2 = sum of (x minus x-bar) squared, divided by (n minus 1). Population variance: sigma^2 = sum of (x minus mu) squared, divided by n. In both cases, x-bar or mu is the mean and n is the count of values. Standard deviation is the square root of variance.