Mean Absolute Deviation Calculator
Free mean absolute deviation (MAD) calculator. Compute MAD about mean or median, compare to SD, see
Why This Statistical Analysis Matters
Why: Statistical calculator for analysis.
How: Enter inputs and compute results.
Mean Absolute Deviation — MAD about Mean or Median
Robust alternative to SD. MAD about mean vs median. Relationship to standard deviation. Relative MAD for cross-dataset comparison.
Real-World Scenarios — Click to Load
Data Input
MAD vs SD Comparison
Data Values with Center Line
Absolute Deviations |xᵢ − center|
Calculation Breakdown
For educational and informational purposes only. Verify with a qualified professional.
Key Takeaways
- • MAD about mean: MAD_mean = Σ|xᵢ − x̄|/n — average absolute deviation from the mean
- • MAD about median: MAD_median = Σ|xᵢ − median|/n — robust to outliers
- • Relationship to SD: For normal distributions, MAD ≈ 0.7979 × SD
- • Relative MAD: MAD/mean × 100% — compare variability across scales
- • Use MAD when: Data has outliers; you want a robust measure of spread
Did You Know?
How MAD Works
Step 1: Choose a Center
Use the mean (x̄) or the median. Mean is standard; median is more robust.
Step 2: Compute Deviations
For each value xᵢ, find |xᵢ − center|. Absolute value ensures all deviations are positive.
Step 3: Average the Deviations
MAD = Σ|xᵢ − center| / n. This gives the average distance from the center.
MAD vs Standard Deviation
| Property | MAD | SD |
|---|---|---|
| Uses | Absolute deviations | Squared deviations |
| Outlier sensitivity | Robust | Sensitive |
| Units | Same as data | Same as data |
| For normal data | MAD ≈ 0.7979 × SD | SD |
Expert Tips
When to Use MAD
Use MAD when your data has outliers or is skewed. SD can be inflated by a few extreme values.
Mean vs Median Center
MAD about median is more robust. MAD about mean matches the classical definition and relates to SD.
Frequently Asked Questions
What is the relationship between MAD and SD for normal data?
For a normal distribution, MAD ≈ 0.7979 × SD. The constant √(2/π) ≈ 0.7979 comes from the expected value of |X−μ| when X is standard normal.
Why use MAD instead of standard deviation?
MAD is robust to outliers. A single extreme value can greatly inflate SD, but has limited effect on MAD. Use MAD when your data may contain outliers.
What is relative MAD?
Relative MAD = (MAD / mean) × 100%. It allows comparing variability across datasets with different units or scales, similar to the coefficient of variation.
MAD about mean vs median?
MAD about the median is always ≤ MAD about the mean. The median minimizes the sum of absolute deviations. Use median when you want maximum robustness.
Can MAD be zero?
Yes. MAD is zero when all values are identical (no variation).
How does MAD compare to IQR?
Both are robust. IQR uses quartiles; MAD uses absolute deviations from center. MAD is simpler to interpret as an average distance.
MAD by the Numbers
Official Data Sources
Disclaimer: MAD is a robust measure of spread. For normally distributed data, the 0.7979 factor relates MAD to SD. Use appropriate measures for your data distribution.
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