The variance is the average of the squared deviations about the mean for a set of numbers. The population variance is denoted by . It is given by the formula:
The capital Greek letter sigma is commonly used in mathematics to represent a summation of all the numbers in a grouping.
N is the number of terms in the population.
The following video shows how to calculate the variance of a population.
Variance as a measure of, on average, how far the data points in a population are from the population mean.
The sample variance is denoted by s2. The main use for sample variances is as estimators of population variances. The computation of the sample variance differs slightly from computation of the population variance. The sample variance uses n – 1 in the denominator instead of n because using n in the denominator of a sample variance results in a statistic that tends to underestimate the population variance. (This is further explained in the video below)
The formula for sample variance is:
The following video shows how to use the variance of a sample to estimate the variance of a population.
Sometimes, books may give different formulas for variance.
We will now show how to derive these different formulas for variance.
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.