Absolute Deviation Calculator
Calculate mean or median absolute deviation to measure data spread
Table of Contents
How to Use
- Enter your data values separated by commas, spaces, or semicolons
- Choose deviation type: from mean or from median
- Click calculate to see the absolute deviation results
- Review the MAD, total absolute deviation, mean, and median
What is Absolute Deviation?
Absolute deviation is a measure of how spread out numbers in a dataset are. It calculates the average distance of each data point from a central value (mean or median), using absolute values to avoid negative numbers canceling out positive ones.
The Mean Absolute Deviation (MAD) provides a robust measure of variability that is less sensitive to extreme values compared to standard deviation.
Types of Absolute Deviation
There are two common types of absolute deviation:
- Mean Absolute Deviation: Measures the average distance from the arithmetic mean. Formula: MAD = Σ|xi - mean| / n
- Median Absolute Deviation: Measures the average distance from the median. More robust against outliers. Formula: MAD = Σ|xi - median| / n
Interpreting Results
- Lower MAD: Data points are closer to the center, indicating less variability
- Higher MAD: Data points are more spread out, indicating greater variability
- MAD of 0: All data points are identical
- Total Absolute Deviation: Sum of all individual deviations, useful for understanding overall spread
Applications
- Quality control: Monitoring consistency in manufacturing processes
- Financial analysis: Measuring portfolio volatility and risk
- Weather forecasting: Analyzing temperature variations
- Sports statistics: Evaluating player consistency
- Research: Measuring experimental error and reliability
- Machine learning: Feature scaling and anomaly detection
MAD vs Standard Deviation
While both measure spread, they have key differences:
- MAD uses absolute values; standard deviation uses squared differences
- MAD is more robust to outliers
- Standard deviation is more commonly used in statistical inference
- MAD is easier to interpret intuitively
- Standard deviation has better mathematical properties for theoretical work
Frequently Asked Questions
- What's the difference between mean and median absolute deviation?
- Mean absolute deviation measures distance from the arithmetic mean, while median absolute deviation measures distance from the median. Median absolute deviation is more resistant to extreme outliers and provides a more robust measure of variability.
- When should I use MAD instead of standard deviation?
- Use MAD when your data contains outliers or when you need a more intuitive measure of spread. MAD is less influenced by extreme values compared to standard deviation, which squares the differences.
- Can absolute deviation be zero?
- Yes, MAD equals zero only when all data points are identical (no variability). This indicates perfect consistency in the dataset.
- How do I interpret a large MAD value?
- A large MAD indicates high variability - data points are spread far from the center. In context, this could mean inconsistent measurements, high volatility, or diverse values depending on your application.