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, providing a measure of data dispersion.

3. Importance of Variance Calculation

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

4. Using the Calculator

Tips: Enter numeric values separated by commas (e.g., 5, 7, 8, 9). The calculator will ignore any non-numeric values in the input.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between variance and standard deviation?
A: Standard deviation is the square root of variance. While variance gives squared units, standard deviation returns to the original units of measurement.

Q2: When should I use population variance vs sample variance?
A: Use population variance when working with complete datasets, and sample variance (dividing by n-1) when working with samples of larger populations.

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

Q4: Can variance be negative?
A: No, since it's calculated from squared differences, variance is always non-negative.

Q5: How is variance used in real-world applications?
A: Variance is used in finance to measure risk, in quality control to assess process consistency, and in scientific research to evaluate data reliability.