Variance Calculator: Find Sample & Population Variance

Variance & Standard Deviation Calculator

Enter a set of numbers separated by commas or spaces to instantly calculate sample and population variance.

Dataset (comma or space separated):

STATISTICAL ANALYSIS OUTPUT

Sample Variance ($s^2$): 0.0000

Standard Deviation ($s$): 0.0000

Mean: 0.00 | Count ($n$): 0

What is Variance in Statistics?

In statistics, **variance** measures how far each number in a dataset is from the mean (average) and thus from every other number in the set. It is a fundamental indicator of data dispersion. A small variance indicates that data points are clustered closely around the mean, while a high variance shows that data points are spread out widely across a broader range.

Our online **Variance Calculator** is built using high-performance, lightweight vanilla JavaScript designed with strict adherence to Web Accessibility and Core Web Vitals standards, ensuring instant execution and top-tier search engine indexing.

Formulas for Sample and Population Variance

Depending on whether your dataset represents an entire population or just a sample, the formulas differ slightly:

Sample Variance ($s^2$):
- $s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}$

Population Variance ($\sigma^2$):
- $\sigma^2 = \frac{\sum (x_i - \mu)^2}{N}$

Frequently Asked Questions (Frequently Searched User Questions)

Q: What is the difference between sample variance and population variance?
A: Sample variance divides the sum of squared differences by $n - 1$ (Bessel's correction) because we are estimating population parameters from a subset. Population variance divides by the total count $N$ since the entire data is known.

Q: How is standard deviation related to variance?
A: Standard deviation is simply the square root of the variance. While variance is measured in squared units, standard deviation returns to the original units of the data.