Median Absolute Deviation Calculator
Calculate MAD to measure data spread around the median
Calculate Median Absolute Deviation
Enter numerical values one by one. New fields will appear automatically as needed.
Enter Your Data
Please enter at least one numerical value to calculate the Median Absolute Deviation.
Example: Running Race Times
Race Results (seconds)
Sorted: 11, 12, 12, 14, 15, 16
Step 1: Find Median
6 values (even count)
Middle values: 12 and 14
Median: (12 + 14) รท 2 = 13
Step 2: Calculate Deviations
11-13=-2, 12-13=-1, 12-13=-1
14-13=1, 15-13=2, 16-13=3
Step 3: Absolute Values
Absolute deviations: 2, 1, 1, 1, 2, 3
Sorted: 1, 1, 1, 2, 2, 3
Step 4: Find MAD
Middle values: 1 and 2
MAD: (1 + 2) รท 2 = 1.5
Interpretation
The MAD of 1.5 seconds means that, on average, the running times deviate by 1.5 seconds from the median time of 13 seconds. This indicates moderate consistency in performance.
MAD vs Other Measures
When to Use MAD
Quick Tips
MAD is the median of absolute deviations from the median
More robust to outliers than standard deviation
Lower MAD means less variability around median
Useful for non-normal and skewed distributions
Understanding Median Absolute Deviation (MAD)
What is MAD?
Median Absolute Deviation (MAD) measures how spread out data points are from the median. It calculates the median of the absolute differences between each data point and the dataset median, providing a robust measure of variability.
Why Use MAD?
- โขResistant to outliers and extreme values
- โขWorks well with non-normal and skewed data
- โขEasy to interpret and understand
- โขProvides robust statistical analysis
MAD Calculation Steps
Formula: MAD = median(|Xi - median(X)|) where Xi are individual data points.
Real-World Applications
๐โโ๏ธ Sports Performance
Analyze consistency in athletic performance times, race results, or scoring patterns.
performance consistency
๐ Financial Data
Measure variability in stock prices, returns, or other financial metrics with outliers.
market anomalies
๐ฌ Scientific Data
Analyze experimental results, measurement precision, or sensor data reliability.
measurement analysis