1. What is Population Variance?

Population variance (σ²) measures how far each number in a population is from the mean (μ) and thus from every other number in the set. It's the average of the squared differences from the mean.

2. How Does the Calculator Work?

The calculator uses the population variance formula:

Where:

• \( \sigma^2 \) — Population variance
• \( x \) — Individual value in the population
• \( \mu \) — Population mean
• \( N \) — Total number of values in the population

Explanation: The formula calculates the average of the squared differences between each data point and the population mean.

3. Importance of Population Variance

Details: Population variance is a fundamental measure of dispersion in statistics. It quantifies how spread out the values in a population are and is used in many statistical analyses and probability distributions.

4. Using the Calculator

Tips: Enter numerical values separated by commas (e.g., 5, 7, 8, 9, 10). The calculator will compute both the population mean and variance.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between population and sample variance?
A: Population variance divides by N (population size) while sample variance divides by n-1 (sample size minus one) to correct for bias.

Q2: What are the units of population 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 population variance?
A: Use population variance when you have data for the entire population, not just a sample.

Q4: What does a variance of zero mean?
A: A variance of zero indicates all values in the population are identical.

Q5: How is variance related to standard deviation?
A: Standard deviation is the square root of variance, providing dispersion in the original units.