Variance Calculator

Calculate the variance, standard deviation, and mean of your dataset. Enter your numbers separated by commas, spaces, or line breaks to get instant statistical results.

Enter Numbers (separated by commas, spaces, or new lines)

How to Use the Variance Calculator

Enter your dataset numbers in the text area above
Numbers can be separated by commas, spaces, or placed on separate lines
Click the "Calculate Variance" button
View the calculated mean, variance, and standard deviation

Understanding Variance

Variance is a statistical measure that tells you how spread out numbers are in a dataset. It measures the average squared deviation from the mean.

Mean: The average of all numbers in the dataset
Variance: The average of the squared differences from the mean
Standard Deviation: The square root of variance, in the same units as the data

Variance Formula

The variance is calculated using the following formula:

Variance = Σ(x - μ)² / n

Where:

x = each value in the dataset
μ = mean of the dataset
n = number of values in the dataset
Σ = sum of all values

Sample Variance Formula:

Sample Variance = Σ(x - x̄)² / (n - 1)

For sample data, we divide by (n-1) instead of n (Bessel's correction)

Applications of Variance

Quality control in manufacturing: Monitor consistency in production
Financial risk assessment: Measure investment volatility
Scientific research and data analysis: Evaluate data spread
Performance evaluation and benchmarking: Compare consistency
Portfolio management and investment analysis: Assess risk levels

Population vs Sample Variance

Population Variance: Used when you have data for an entire population. Divides by n.

Sample Variance: Used when you have a sample from a larger population. Divides by (n-1) to provide an unbiased estimate.

This calculator computes both types for your reference.