1. What are Measures of Dispersion?

Definition: Measures of dispersion describe how spread out or varied a set of data is.

Purpose: They help quantify the variability in data, complementing measures of central tendency like the mean.

2. How Does the Calculator Work?

The calculator computes three key dispersion measures:

Where:

• σ² — Variance (average of squared differences from mean)
• σ — Standard deviation (square root of variance)
• R — Range (difference between max and min values)
• x — Individual data points
• μ — Mean of the data
• N — Number of data points

3. Importance of Dispersion Measures

Details: Understanding dispersion helps in assessing data reliability, comparing datasets, and making statistical inferences.

4. Using the Calculator

Tips: Enter numeric values separated by commas. The calculator will ignore any 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 original units, making SD more interpretable.

Q2: When should I use range vs standard deviation?
A: Range is simpler but affected by outliers. SD considers all data points but assumes normal distribution.

Q3: What does a high standard deviation indicate?
A: It means data points are spread out widely from the mean, showing high variability.

Q4: Can I calculate these for a sample instead of population?
A: For samples, divide by N-1 (not N) for unbiased variance estimation (Bessel's correction).

Q5: How do outliers affect these measures?
A: Range is most affected. Variance and SD are somewhat affected as they use squared differences.