1. What is Variance?

Variance is a measure of how spread out numbers are in a dataset. It represents the average of the squared differences from the mean. The formula calculates sample variance (using n-1 denominator).

2. How Does the Calculator Work?

The calculator uses the variance equation:

Where:

• \( x_i \) — Individual data points
• \( \bar{x} \) — Mean of the data
• \( n \) — Number of data points

Explanation: The equation calculates the average of squared deviations from the mean, with n-1 denominator for sample variance (Bessel's correction).

3. Importance of Variance Calculation

Details: Variance is fundamental in statistics for measuring dispersion. It's used in statistical tests, quality control, risk assessment, and many other applications.

4. Using the Calculator

Tips: Enter your numerical data separated by commas (e.g., 1, 2, 3, 4, 5). You need at least 2 data points to calculate variance.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between population and sample variance?
A: Population variance divides by n, while sample variance divides by n-1 (Bessel's correction for unbiased estimation).

Q2: What are the units of variance?
A: Variance is in squared units of the original data (e.g., if data is in meters, variance is in meters²).

Q3: When should I use variance vs standard deviation?
A: Variance is mathematically fundamental, while standard deviation (square root of variance) is more interpretable as it's in original units.

Q4: What does high variance indicate?
A: High variance means data points are spread out widely from the mean and from each other.

Q5: Can variance be negative?
A: No, variance is always non-negative since it's a sum of squared quantities.