Variance Calculator
Calculate the variance of your data set with ease. This calculator computes both population and sample variance, standard deviation, mean, and provides a detailed step-by-step breakdown of the calculation. Perfect for students, researchers, and data analysts.
What Is Variance?
Variance is a measure of how far a set of numbers are spread out from their mean (average). It is calculated as the average of the squared differences from the mean. Variance is one of the most important concepts in statistics and is used in finance, science, engineering, and social sciences to measure variability and risk.
Population vs. Sample Variance
There are two types of variance:
- Population Variance (σ²): Used when you have data for every member of the population. Formula: σ² = Σ(xᵢ − μ)² / N
- Sample Variance (s²): Used when you only have a sample of the population. Formula: s² = Σ(xᵢ − x̄)² / (n − 1)
The sample variance uses n − 1 in the denominator (Bessel's correction) to provide an unbiased estimate of the population variance.
How to Calculate Variance
- Find the Mean: Add all numbers and divide by the count.
- Calculate Deviations: Subtract the mean from each number.
- Square the Deviations: Square each deviation to eliminate negative values.
- Find the Mean of Squared Deviations: For population: divide by N. For sample: divide by n − 1.
Why Use This Variance Calculator?
- Both Population & Sample: Get both results in one calculation.
- Step-by-Step Breakdown: See exactly how the calculation works.
- Visual Charts: Understand your data distribution with interactive charts.
- Flexible Data Entry: Add numbers individually or paste entire datasets.
- Free & Private: No registration, no data storage.
❓ Variance Calculator FAQ
What is variance?
Variance is a measure of how spread out the numbers in a data set are. It is the average of the squared differences from the mean.
What is the difference between population and sample variance?
Population variance (σ²) uses all data points and divides by N. Sample variance (s²) uses n − 1 (Bessel's correction) to provide an unbiased estimate when working with a sample of a larger population.
What is Bessel's correction?
Bessel's correction is the use of n − 1 instead of n in the denominator when calculating sample variance. It corrects the bias in the estimation of the population variance from a sample.
What does a low variance mean?
A low variance means the data points are clustered closely around the mean, indicating low variability and high consistency in the data.
What does a high variance mean?
A high variance means the data points are spread out over a wide range, indicating high variability and less consistency in the data.
How is variance used in finance?
In finance, variance is used as a measure of risk and volatility. A higher variance indicates higher risk and greater price fluctuations.
Can variance be negative?
No, variance is always a non-negative number. It is zero only when all data points are identical.
What is the relationship between variance and standard deviation?
Standard deviation is the square root of the variance. Standard deviation is often preferred because it is in the same units as the original data.
How do I interpret the variance value?
The variance tells you the average squared distance of each data point from the mean. Because it uses squared units, it can be harder to interpret than standard deviation, which is in the original units.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required. All calculations are performed in your browser.