Mean Absolute Deviation Calculator by Omni
Try this mean absolute deviation (MAD) calculator to measures the average distance between each data point and the mean of a dataset.
The MAD is calculated through the following steps:
- Calculate the mean of the dataset.
- Find the absolute difference between each value and the mean.
- Calculate the average of these absolute differences.
Dataset: 10, 12, 14, 16, 18
- Calculate mean: (10 + 12 + 14 + 16 + 18) ÷ 5 = 14
- Find absolute differences from mean:
- |10 – 14| = 4
- |12 – 14| = 2
- |14 – 14| = 0
- |16 – 14| = 2
- |18 – 14| = 4
- Calculate MAD: (4 + 2 + 0 + 2 + 4) ÷ 5 = 2.4
The MAD of 2.4 indicates that, on average, the values in the dataset deviate from the mean by 2.4 units.
How do you calculate the mean absolute deviation?
To calculate MAD:
- Find the mean of the dataset
- Calculate the absolute difference between each data point and the mean
- Sum these absolute differences
- Divide the sum by the number of data points
Consider the dataset [2, 4, 6, 8, 10]
Calculate the mean: (2 + 4 + 6 + 8 + 10) / 5 = 6
Find absolute differences: |2-6| = 4, |4-6| = 2, |6-6| = 0, |8-6| = 2, |10-6| = 4
Sum the differences: 4 + 2 + 0 + 2 + 4 = 12
Divide by the number of data points: 12 / 5 = 2.4
The mean absolute deviation for this dataset is 2.4.
The mean absolute deviation (MAD) is a measure of variability in a dataset that quantifies the average distance between each data point and the mean. Unlike variance or standard deviation, MAD uses absolute values, making it less sensitive to outliers.
Mean Absolute Deviation Calculation Chart
| Data Point | Deviation from Mean | Absolute Deviation |
|---|---|---|
| 2 | 2 – 6 = -4 | 4 |
| 4 | 4 – 6 = -2 | 2 |
| 6 | 6 – 6 = 0 | 0 |
| 8 | 8 – 6 = 2 | 2 |
| 10 | 10 – 6 = 4 | 4 |
| Sum | 12 | |
| MAD | 12 / 5 = 2.4 |
Mean Absolute Deviation Calculation Formula
The formula for calculating the Mean Absolute Deviation MAD is:
MAD = Σ|x - μ| / NWhere:
- Σ represents the sum
- x is each individual value in the dataset
- μ (mu) is the mean of the dataset
- N is the number of values in the dataset
- |x – μ| represents the absolute value of the difference between x and μ
Using our previous example:
MAD = (|2-6| + |4-6| + |6-6| + |8-6| + |10-6|) / 5 = (4 + 2 + 0 + 2 + 4) / 5 = 12 / 5 = 2.4Related Statistics Tools