1. What Is Variance?

Variance is a statistical measurement of the spread between numbers in a data set. It measures how far each number in the set is from the mean and thus from every other number in the set.

2. How Does The Calculator Work?

The calculator uses the sample variance formula:

Where:

• \( x_i \) — Individual values in the dataset
• \( \mu \) — Mean of all values
• \( N \) — Number of values in the dataset

Explanation: The formula calculates the average of the squared differences from the mean, using N-1 for sample variance to account for bias in estimation.

3. Importance Of Variance Calculation

Details: Variance is crucial in statistics for measuring dispersion, understanding data variability, and forming the basis for other statistical measures like standard deviation.

4. Using The Calculator

Tips: Enter numerical values separated by commas. The calculator will compute the sample variance. Minimum 2 values are required for calculation.

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 to correct for bias when estimating population variance from a sample.

Q2: When should I use sample variance vs population variance?
A: Use sample variance when working with a subset of data representing a larger population. Use population variance when you have data for the entire population.

Q3: What does a high variance indicate?
A: High variance indicates that data points are spread out widely around the mean, suggesting greater variability in the dataset.

Q4: How is variance related to standard deviation?
A: Standard deviation is the square root of variance, providing a measure of spread in the same units as the original data.

Q5: Can variance be negative?
A: No, variance cannot be negative since it's calculated from squared differences, which are always non-negative.