Mean Absolute Deviation Calculator

How to Calculate Mean Absolute Deviation

The Mean Absolute Deviation (MAD) is a measure of variability in a dataset that calculates the average distance between each data point and the mean. It provides insight into the spread of the data.

Formula

The formula for calculating the Mean Absolute Deviation is:

\[ MAD = \frac{\sum_{i=1}^{n} |x_i - \bar{x}|}{n} \]

Where:

• \(x_i\) represents each value in the dataset
• \(\bar{x}\) is the mean of the dataset
• \(n\) is the number of values in the dataset

Calculation Steps

1. Calculate the mean of the dataset
2. Calculate the absolute difference between each data point and the mean
3. Sum up all the absolute differences
4. Divide the sum by the number of data points

Example

Let's calculate the Mean Absolute Deviation for the dataset: 4, 6, 8, 6, 5, 3, 8

1. Calculate the mean: \(\bar{x} = \frac{4 + 6 + 8 + 6 + 5 + 3 + 8}{7} = 5.71\)
2. Calculate absolute deviations: |4 - 5.71| = 1.71, |6 - 5.71| = 0.29, |8 - 5.71| = 2.29, |6 - 5.71| = 0.29, |5 - 5.71| = 0.71, |3 - 5.71| = 2.71, |8 - 5.71| = 2.29
3. Sum the absolute deviations: 1.71 + 0.29 + 2.29 + 0.29 + 0.71 + 2.71 + 2.29 = 10.29
4. Divide by the number of data points: 10.29 / 7 = 1.47

Therefore, the Mean Absolute Deviation is 1.47.

Visual Representation

This diagram illustrates the Mean Absolute Deviation for the example dataset. The green line represents the mean, blue dots are data points, and red dashed lines show the deviations from the mean.