1. What are Measures of Dispersion?

Definition: Measures of dispersion describe how spread out a dataset is. They complement measures of central tendency like the mean.

Purpose: These measures help understand the variability in data, which is crucial for statistical analysis and decision making.

2. Key Measures of Dispersion

The calculator provides four main measures:

Where:

• \( \sigma^2 \) — Variance (average squared deviation from mean)
• \( \sigma \) — Standard deviation (square root of variance)
• \( R \) — Range (difference between max and min values)
• \( x \) — Individual data points
• \( \mu \) — Mean of the data
• \( N \) — Number of data points

3. Importance of Dispersion Measures

Details: Understanding dispersion helps assess data reliability, compare datasets, and identify outliers or unusual patterns.

4. Using the Calculator

Tips: Enter comma-separated numerical values (e.g., "5, 7, 12, 6, 9"). The calculator will compute all dispersion measures automatically.

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 would I use range vs standard deviation?
A: Range is simpler but affected by outliers. Standard deviation considers all data points but is more complex.

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

Q4: Can I calculate these for a sample instead of population?
A: For samples, divide by N-1 (not N) for variance. This calculator uses population formulas.

Q5: How do outliers affect these measures?
A: Outliers significantly increase range and variance. Consider examining your data for outliers.