Mean Absolute Deviation Calculator
Calculate the mean absolute deviation of your dataset
Table of Contents
How to Use
- Enter your data values separated by spaces, commas, or semicolons
- Click calculate to find the mean absolute deviation
- Review the detailed breakdown of deviations from the mean
- Use the results to understand data spread and consistency
What is Mean Absolute Deviation?
Mean Absolute Deviation (MAD) is a statistical measure that quantifies the average distance between each data point and the mean of a dataset. Unlike standard deviation, MAD uses absolute values, making it easier to interpret and less sensitive to outliers.
MAD is particularly useful when you want to understand the typical deviation from the mean without the complexity of squared values used in standard deviation.
Formula and Calculation
The formula for Mean Absolute Deviation is:
MAD = Σ|xᵢ - μ| / n
Where:
- xᵢ represents each individual data point
- μ is the mean of all data points
- n is the number of data points
- Σ indicates summation of all absolute deviations
Interpreting MAD Values
Understanding MAD values:
- Small MAD: Data points are clustered close to the mean
- Large MAD: Data points are spread out from the mean
- MAD = 0: All data points are identical
- MAD is always non-negative
MAD provides an intuitive measure of spread that's directly comparable to the original data units.
Advantages of MAD
- Easy to understand and interpret
- Less sensitive to outliers than standard deviation
- Uses the same units as the original data
- Provides a robust measure of variability
- Useful for quality control and process monitoring
Frequently Asked Questions
- What's the difference between MAD and standard deviation?
- MAD uses absolute deviations while standard deviation uses squared deviations. MAD is more intuitive and less affected by extreme values, while standard deviation gives more weight to large deviations.
- When should I use MAD instead of standard deviation?
- Use MAD when you want a more robust measure of spread that's less sensitive to outliers, or when you need an easily interpretable measure in the same units as your data.
- Can MAD be negative?
- No, MAD is always non-negative since it uses absolute values. A MAD of 0 means all data points are identical to the mean.
- How is MAD different from range?
- Range only considers the extreme values (max - min), while MAD considers the average distance of all points from the mean, making it a more comprehensive measure of spread.
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