1. What is Variance?

Variance is a measure of how far a set of numbers are spread out from their average value. It quantifies the degree of variation or dispersion in a dataset.

2. How Does the Calculator Work?

The calculator uses the variance formula:

Where:

• \( x_i \) — Individual data points
• \( \text{Mean} \) — Average of all data points
• \( n \) — Number of data points

Explanation: The formula calculates the average of the squared differences from the mean.

3. Importance of Variance Calculation

Details: Variance is fundamental in statistics for measuring dispersion, assessing risk in finance, quality control in manufacturing, and many other applications.

4. Using the Calculator

Tips: Enter numerical values separated by commas. Example: "5, 7, 8, 9, 10". The calculator will ignore non-numeric values.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between variance and standard deviation?
A: Standard deviation is the square root of variance. Both measure spread but standard deviation is in the same units as the original data.

Q2: When should I use population variance vs sample variance?
A: Use population variance when working with complete data. For samples, divide by n-1 (Bessel's correction) to get unbiased estimate.

Q3: What does a variance of zero mean?
A: All values in the dataset are identical (no variability).

Q4: Can variance be negative?
A: No, since it's an average of squared values, variance is always non-negative.

Q5: How does variance relate to the mean?
A: Variance measures how far data points are from the mean, but the mean itself doesn't determine variance - the spread does.