1. What is Dispersion?

Dispersion measures how spread out a set of data is. The two main measures are variance and standard deviation. Variance is the average of the squared differences from the mean, while standard deviation is the square root of variance.

2. How Does the Calculator Work?

The calculator uses these formulas:

Where:

• \( x_i \) — Individual data points
• \( \bar{x} \) — Mean of all data points
• \( n \) — Number of data points

3. Importance of Dispersion Measures

Details: Dispersion measures are crucial for understanding data variability. They help in risk assessment, quality control, and comparing different data sets.

4. Using the Calculator

Tips: Enter numerical values separated by commas. Select whether you want to calculate variance or standard deviation. At least two data points are recommended.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between variance and standard deviation?
A: Variance is in squared units while standard deviation is in the original units, making it more interpretable.

Q2: When should I use variance vs standard deviation?
A: Standard deviation is more commonly used for reporting, while variance is more fundamental in statistical calculations.

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

Q4: Are there other measures of dispersion?
A: Yes, including range, interquartile range, and mean absolute deviation, but variance and SD are most common.

Q5: How does sample size affect dispersion measures?
A: Larger samples tend to give more stable estimates of population dispersion.