Median Absolute Deviation Calculator

Calculate MAD to measure data spread around the median

Calculate Median Absolute Deviation

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Example: Running Race Times

Race Results (seconds)

Running times: 12, 16, 12, 11, 14, 15

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

๐Ÿ“Š
MAD (Median-based)
Uses median, robust to outliers
๐Ÿ“ˆ
MAD (Mean-based)
Uses mean, affected by outliers
๐Ÿ“‰
Standard Deviation
Squares deviations, outlier sensitive
๐Ÿ“
Range
Simple spread measure

When to Use MAD

Non-normal Data
When data isn't normally distributed
Outlier Presence
When extreme values exist
Robust Statistics
Need outlier-resistant measure
Skewed Distributions
For asymmetric data patterns

Quick Tips

โœ“

MAD is the median of absolute deviations from the median

โœ“

More robust to outliers than standard deviation

โœ“

Lower MAD means less variability around median

โœ“

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?

  • โ€ขResistant to outliers and extreme values
  • โ€ขWorks well with non-normal and skewed data
  • โ€ขEasy to interpret and understand
  • โ€ขProvides robust statistical analysis

MAD Calculation Steps

Step 1: Find Median
Sort data and find the middle value
Step 2: Calculate Deviations
Subtract median from each data point
Step 3: Take Absolute Values
Make all deviations positive
Step 4: Find Median of Absolute Deviations
Sort and find middle value = MAD

Formula: MAD = median(|Xi - median(X)|) where Xi are individual data points.

Real-World Applications

๐Ÿƒโ€โ™‚๏ธ Sports Performance

Analyze consistency in athletic performance times, race results, or scoring patterns.

MAD helps identify
performance consistency

๐Ÿ“ˆ Financial Data

Measure variability in stock prices, returns, or other financial metrics with outliers.

Robust against
market anomalies

๐Ÿ”ฌ Scientific Data

Analyze experimental results, measurement precision, or sensor data reliability.

Outlier-resistant
measurement analysis