1. What is Sample Mean and Variance?

The sample mean is the average value of a set of numbers, while the sample variance measures how far each number in the set is from the mean and thus from every other number in the set. These are fundamental statistics for describing data distribution.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Where:

• \( x_i \) — Individual data points
• \( n \) — Number of data points in the sample
• \( \text{Mean} \) — Arithmetic average of the data

Explanation: The mean gives the central tendency of the data, while variance measures the spread of the data points around the mean.

3. Importance of Mean and Variance

Details: Mean and variance are fundamental descriptive statistics used in virtually all statistical analyses. They form the basis for more complex statistical measures and tests.

4. Using the Calculator

Tips: Enter your numerical data points separated by commas. The calculator will ignore any non-numeric values. You need at least 2 data points to calculate variance.

5. Frequently Asked Questions (FAQ)

Q1: Why is variance divided by n-1 instead of n?
A: Dividing by n-1 (Bessel's correction) gives an unbiased estimate of the population variance when calculating from a sample.

Q2: What's the difference between variance and standard deviation?
A: Standard deviation is the square root of variance. Both measure spread, but standard deviation is in the same units as the original data.

Q3: When should I use population variance instead?
A: Use population variance (divided by n) only when you have data for the entire population, not just a sample.

Q4: How many data points do I need?
A: For meaningful variance, at least 2 points are needed. More points give more reliable estimates.

Q5: What if my data contains outliers?
A: Variance is sensitive to outliers. Consider examining your data for outliers before interpreting variance.