Home Back

Measures of Dispersion Calculator

Dispersion Formulas:

\[ \sigma^2 = \frac{\sum(x - \mu)^2}{N} \] \[ \sigma = \sqrt{\sigma^2} \] \[ R = max - min \]

Unit Converter ▲

Unit Converter ▼

From: To:

1. What is Measures of Dispersion?

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

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

2. Key Measures of Dispersion

The calculator provides three main measures:

\[ \sigma^2 = \frac{\sum(x - \mu)^2}{N} \] \[ \sigma = \sqrt{\sigma^2} \] \[ R = max - min \]

Where:

3. Importance of Dispersion Measures

Details: Understanding dispersion helps assess data reliability, compare datasets, and make informed decisions in statistics.

4. Using the Calculator

Tips: Enter numeric values separated by commas (e.g., "5, 10, 15, 20"). 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 should I use range vs standard deviation?
A: Range gives a quick sense of spread but is sensitive to outliers. Standard deviation provides more reliable measure of typical variation.

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

Q4: Can I use this for population and sample data?
A: This calculator uses population formulas. For sample data, divide by N-1 instead of N for variance.

Q5: How do outliers affect these measures?
A: Outliers significantly impact range and moderately affect variance/standard deviation.

Measures of Dispersion Calculator© - All Rights Reserved 2025