1. What Are Measures of Dispersion?

Definition: Measures of dispersion describe how spread out a dataset is from its central value (usually the mean).

Purpose: They help statisticians and researchers understand the variability in data, which is crucial for making accurate conclusions.

2. Key Measures of Dispersion

The calculator provides three 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: While measures of central tendency (mean, median) show where data centers, dispersion measures show how reliable that center is and how much variation exists.

4. Using the Calculator

Tips: Enter numeric values separated by commas (e.g., "5, 8, 12, 3, 9"). The calculator will ignore non-numeric values.

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 gives a quick sense of spread but is affected by outliers. Standard deviation gives a more robust measure of typical variation.

Q3: What does a high standard deviation indicate?
A: It means data points are generally far from the mean, showing high variability in the dataset.

Q4: Can I calculate these for a sample instead of a population?
A: For samples, divide by N-1 instead of N for variance (Bessel's correction). This calculator uses population formulas.

Q5: How do outliers affect these measures?
A: Outliers significantly affect range and variance. Standard deviation is less affected but still influenced by extreme values.