๐ก๏ธ Median Absolute Deviation Calculator
Measure robust spread using the median absolute deviation, which is less sensitive to outliers than standard deviation.
๐ Statistics๐ Formula included๐ง Practice questionsโ Free
Please enter valid values.
Formula and Explanation
Measure robust spread using the median absolute deviation, which is less sensitive to outliers than standard deviation.
| Concept | Formula or rule |
|---|---|
| Median Absolute Deviation Calculator | MAD = median(|xแตข โ median(x)|) |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: For 1, 2, 3, 4, 100, the median is 3 and the absolute deviations are 2, 1, 0, 1, 97.
โ MAD = median(0, 1, 1, 2, 97) = 1
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
โ ๏ธ
Using the mean instead of the median
The standard MAD is centered on the median.
The standard MAD is centered on the median.
โ ๏ธ
Forgetting absolute values
Negative and positive deviations must both become positive.
Negative and positive deviations must both become positive.
โ ๏ธ
Confusing MAD with mean absolute deviation
They are related but use different centers and summary statistics.
They are related but use different centers and summary statistics.
Practice Questions
1. Find MAD for 1, 1, 2, 2, 100.
Answer: 1
2. Find MAD for 5, 5, 5.
Answer: 0
3. Which is more resistant to outliers: MAD or standard deviation?
Answer: MAD.
Frequently Asked Questions
Why is MAD robust?โพ
The median changes little when a few values are extreme.
Can MAD be zero?โพ
Yes, especially when at least half the values equal the median.
How does MAD compare with standard deviation?โพ
For approximately normal data, 1.4826 ร MAD is often used as a robust estimate of standard deviation.