Calculate MAD instantly with our free mean absolute deviation online calculator.
Enter your dataset and get the mean, absolute deviations, and MAD with step-by-step results. Perfect for statistics, finance, and quality control analysis.
Mean Absolute Deviation Calculator
What Is Mean Absolute Deviation (MAD) in Math?
Mean Absolute Deviation (MAD) measures how spread out numbers are from their average. Unlike standard deviation, MAD uses absolute values, making it easier to interpret. It’s widely used in statistics, finance, and quality control.
Why Use MAD?
MAD provides a clear, simple way to measure variability without complex calculations. It’s less affected by extreme values than standard deviation, making it ideal for real-world data.
Example: A teacher analyzing test scores with a low MAD knows most students performed near the average.
Mean Absolute Deviation Formula
Calculation Steps:
- Calculate the mean (x̄) of all data points
- Find the absolute difference between each point and the mean |xi – x̄|
- Sum all these absolute differences
- Divide by the number of data points (n)
How to Calculate Mean Absolute Deviation (Step-by-Step)
- Find the mean → Add all values and divide by the count.
- Calculate deviations → Subtract the mean from each value (ignore negatives).
- Average the deviations → Sum all absolute differences and divide by data count.
Example: What’s the MAD of 6, 2, 8, 4, 8, 6, 8, 8?
- Mean = (6+2+8+4+8+6+8+8)/8 = 6.25
- Deviations = |6-6.25|, |2-6.25|, … → 0.25, 4.25, 1.75, 2.25, 1.75, 0.25, 1.75, 1.75
- MAD = (0.25 + 4.25 + … + 1.75)/8 ≈ 1.75
Try these:
- What’s the MAD of 10, 4, 12, 4, 2, 10, 10, 6?
- Find the MAD of 3, 1, 5, 5, 2, 3, 2, 3, 4, 2.
MAD Calculator for Grouped & Ungrouped Data
Our interactive calculator handles both individual and grouped data. Just input your numbers (e.g., *16, 14, 2, 4, 18, 20, 12, 10*) and get instant results, including:
✅ Mean
✅ Absolute deviations
✅ Final MAD
Looking for a mean absolute deviation calculator with steps? Ours breaks it down for you!
Frequently Asked Questions (FAQs)
1. How do you calculate the mean absolute deviation?
Follow the 3-step method above or use our calculator for instant results.
2. Can MAD be zero?
Yes! A MAD of zero means all data points are identical (no variation).
3. What’s a “good” MAD value?
It depends on context—low MAD means consistent data (e.g., stable test scores).
4. How is MAD used in finance?
Investors use it to measure portfolio risk—lower MAD = more stable returns.
Practice Problems (Answers Below)
Test your skills with these real-world examples:
- Find the MAD of 9, 2, 9, 9, 5, 4, 9, 1, 4, 10.
- Calculate MAD for 16, 14, 2, 4, 18, 20, 12, 10.
Answers:
- MAD ≈ 2.8
- MAD ≈ 5.5
Final Thoughts
The Mean Absolute Deviation Calculator is a fast, easy, and accurate way to understand how your data spreads. Whether you’re a student doing homework, a teacher grading papers, or a data analyst checking variability, this tool provides reliable results instantly.
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