1. What is Variance?

Variance is a measure of dispersion that quantifies how far each number in a dataset is from the mean (average) of the dataset. It represents the average of the squared differences from the mean.

2. How Does the Calculator Work?

The calculator uses the sample variance formula:

Where:

• \( x_i \) — Individual values in the dataset
• \( \text{mean} \) — Average 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 in the denominator for sample variance (Bessel's correction).

3. Importance of Variance Calculation

Details: Variance is fundamental in statistics for measuring data dispersion. It's used in statistical tests, quality control, risk assessment, and many other analytical applications.

4. Using the Calculator

Tips: Enter numerical values separated by commas (e.g., 5, 7, 8, 9). At least two values are required to calculate variance. The calculator automatically filters out non-numeric entries.

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 (Bessel's correction) to reduce bias in small samples.

Q2: Why square the differences in variance calculation?
A: Squaring ensures all differences are positive and gives more weight to larger deviations.

Q3: What does a high variance indicate?
A: High variance means data points are spread out widely from the mean, indicating greater variability in the dataset.

Q4: What are the units of variance?
A: Variance is in squared units of the original data (e.g., if data is in meters, variance is in meters²).

Q5: How is variance related to standard deviation?
A: Standard deviation is the square root of variance, bringing the measure back to the original units.