1. What is Variance of Observations?

Variance is defined as the average of the squared differences from the Mean. It measures how far a set of numbers are spread out from their average value, providing insight into the variability within a dataset.

2. How Does the Calculator Work?

The calculator uses the variance formula:

Where:

• \( \sigma^2 \) — Variance
• \( \sum V^2 \) — Sum of square of residual variation
• \( n_{obs} \) — Number of observations

Explanation: The formula calculates the unbiased estimate of population variance by dividing the sum of squared residuals by the degrees of freedom (n-1).

3. Importance of Variance Calculation

Details: Variance is a fundamental measure of dispersion in statistics. It helps quantify the spread of data points, assess data reliability, and is used in various statistical tests and analyses.

4. Using the Calculator

Tips: Enter the sum of squared residual variations and the number of observations. The number of observations must be at least 2 to calculate variance.

5. Frequently Asked Questions (FAQ)

Q1: Why divide by n-1 instead of n?
A: Dividing by n-1 (Bessel's correction) provides an unbiased estimate of the population variance when working with a sample.

Q2: What's the difference between variance and standard deviation?
A: Variance is the average of squared differences from the mean, while standard deviation is the square root of variance and has the same units as the original data.

Q3: When should I use population variance vs sample variance?
A: Use population variance (dividing by n) when you have data for the entire population. Use sample variance (dividing by n-1) when working with a sample from a larger population.

Q4: Can variance be negative?
A: No, variance cannot be negative since it's calculated from squared values. The minimum possible variance is zero, indicating all values are identical.

Q5: How does variance relate to data distribution?
A: Higher variance indicates greater spread and dispersion of data points, while lower variance suggests data points are clustered closely around the mean.