The Mean Absolute Deviation (MAD) Calculator helps you measure the average distance between each data point and the mean. Unlike variance or standard deviation, MAD uses absolute differences which makes it less sensitive to outliers and provides a more intuitive measure of dispersion in the original units of your data. It's particularly useful for financial analysis, quality control, and analyzing datasets where you want to understand typical deviations without overemphasizing extreme values.
Need a quick calculation? Enter your numbers below, separated by commas:
Mean Absolute Deviation measures the average absolute difference between each data point and the mean of all data points. It's a measure of dispersion in the original units of measurement, making it more intuitive to interpret than variance.
Mean Absolute Deviation Formula:
Where:
Let's calculate the mean absolute deviation for a dataset of daily temperatures (in °C) for a week:
| Day | Temperature (°C) |
|---|---|
| Monday | 22 |
| Tuesday | 20 |
| Wednesday | 25 |
| Thursday | 21 |
| Friday | 23 |
| Saturday | 24 |
| Sunday | 19 |
Step 1: Calculate the mean temperature:
Step 2: Calculate the absolute deviations from the mean:
| Day | Temperature (°C) | Deviation from Mean | Absolute Deviation |
|---|---|---|---|
| Monday | 22 | 22 - 22 = 0 | |0| = 0 |
| Tuesday | 20 | 20 - 22 = -2 | |-2| = 2 |
| Wednesday | 25 | 25 - 22 = 3 | |3| = 3 |
| Thursday | 21 | 21 - 22 = -1 | |-1| = 1 |
| Friday | 23 | 23 - 22 = 1 | |1| = 1 |
| Saturday | 24 | 24 - 22 = 2 | |2| = 2 |
| Sunday | 19 | 19 - 22 = -3 | |-3| = 3 |
Step 3: Calculate the mean of the absolute deviations:
Interpretation: A MAD of 1.71°C indicates the typical deviation from the average temperature during the week. This is particularly useful for understanding temperature variations in concrete, interpretable units.
While both MAD and standard deviation measure dispersion, they have key differences that make each suitable for different situations:
| Feature | Mean Absolute Deviation | Standard Deviation |
|---|---|---|
| Formula | Average of absolute deviations from the mean | Square root of the average squared deviations from the mean |
| Units | Same as original data | Same as original data |
| Outlier Sensitivity | Less sensitive to outliers | More sensitive to outliers (squares the deviations) |
| Mathematical Properties | Less suitable for further statistical inference | Better mathematical properties for inference |
| Interpretation | More intuitive for non-technical audiences | More widely used in advanced statistics |
See how standard deviation (squares) and MAD (lines) treat the same deviations differently. Try adding outliers to see why MAD is less sensitive to extreme values.
Square areas show squared deviations (Standard Deviation) • Line lengths show absolute deviations (MAD)
Square areas represent squared deviations - side length equals deviation distance
Line lengths represent absolute deviations - length equals deviation distance
Each square has side length equal to the deviation distance. The area represents the squared deviation, showing why large deviations become disproportionately influential.
σ = √[Σ(x - μ)² / N]Each line's length represents the absolute deviation. All deviations are treated proportionally to their actual distance from the mean.
MAD = Σ|x - μ| / NTry adding outliers! Notice how the squares' areas grow much faster than the lines' lengths. A point that's 2× further from the mean creates a square with 4× the area, showing why standard deviation is more sensitive to extreme values.
Here is an example of how to calculate the mean absolute deviation of a dataset in R using the tidyverse package. Note that the built-in mad() function in R calculates the median absolute deviation, not the mean absolute deviation.
library(tidyverse)
tips <- read.csv("https://raw.githubusercontent.com/plotly/datasets/master/tips.csv")
mad <- function(x) {
mean(abs(x - mean(x)))
}
mad(tips$tip) # 1.0330The Mean Absolute Deviation (MAD) Calculator helps you measure the average distance between each data point and the mean. Unlike variance or standard deviation, MAD uses absolute differences which makes it less sensitive to outliers and provides a more intuitive measure of dispersion in the original units of your data. It's particularly useful for financial analysis, quality control, and analyzing datasets where you want to understand typical deviations without overemphasizing extreme values.
Need a quick calculation? Enter your numbers below, separated by commas:
Mean Absolute Deviation measures the average absolute difference between each data point and the mean of all data points. It's a measure of dispersion in the original units of measurement, making it more intuitive to interpret than variance.
Mean Absolute Deviation Formula:
Where:
Let's calculate the mean absolute deviation for a dataset of daily temperatures (in °C) for a week:
| Day | Temperature (°C) |
|---|---|
| Monday | 22 |
| Tuesday | 20 |
| Wednesday | 25 |
| Thursday | 21 |
| Friday | 23 |
| Saturday | 24 |
| Sunday | 19 |
Step 1: Calculate the mean temperature:
Step 2: Calculate the absolute deviations from the mean:
| Day | Temperature (°C) | Deviation from Mean | Absolute Deviation |
|---|---|---|---|
| Monday | 22 | 22 - 22 = 0 | |0| = 0 |
| Tuesday | 20 | 20 - 22 = -2 | |-2| = 2 |
| Wednesday | 25 | 25 - 22 = 3 | |3| = 3 |
| Thursday | 21 | 21 - 22 = -1 | |-1| = 1 |
| Friday | 23 | 23 - 22 = 1 | |1| = 1 |
| Saturday | 24 | 24 - 22 = 2 | |2| = 2 |
| Sunday | 19 | 19 - 22 = -3 | |-3| = 3 |
Step 3: Calculate the mean of the absolute deviations:
Interpretation: A MAD of 1.71°C indicates the typical deviation from the average temperature during the week. This is particularly useful for understanding temperature variations in concrete, interpretable units.
While both MAD and standard deviation measure dispersion, they have key differences that make each suitable for different situations:
| Feature | Mean Absolute Deviation | Standard Deviation |
|---|---|---|
| Formula | Average of absolute deviations from the mean | Square root of the average squared deviations from the mean |
| Units | Same as original data | Same as original data |
| Outlier Sensitivity | Less sensitive to outliers | More sensitive to outliers (squares the deviations) |
| Mathematical Properties | Less suitable for further statistical inference | Better mathematical properties for inference |
| Interpretation | More intuitive for non-technical audiences | More widely used in advanced statistics |
See how standard deviation (squares) and MAD (lines) treat the same deviations differently. Try adding outliers to see why MAD is less sensitive to extreme values.
Square areas show squared deviations (Standard Deviation) • Line lengths show absolute deviations (MAD)
Square areas represent squared deviations - side length equals deviation distance
Line lengths represent absolute deviations - length equals deviation distance
Each square has side length equal to the deviation distance. The area represents the squared deviation, showing why large deviations become disproportionately influential.
σ = √[Σ(x - μ)² / N]Each line's length represents the absolute deviation. All deviations are treated proportionally to their actual distance from the mean.
MAD = Σ|x - μ| / NTry adding outliers! Notice how the squares' areas grow much faster than the lines' lengths. A point that's 2× further from the mean creates a square with 4× the area, showing why standard deviation is more sensitive to extreme values.
Here is an example of how to calculate the mean absolute deviation of a dataset in R using the tidyverse package. Note that the built-in mad() function in R calculates the median absolute deviation, not the mean absolute deviation.
library(tidyverse)
tips <- read.csv("https://raw.githubusercontent.com/plotly/datasets/master/tips.csv")
mad <- function(x) {
mean(abs(x - mean(x)))
}
mad(tips$tip) # 1.0330