Mean Absolute Deviation

Finding the mean absolute deviation, also known as the average absolute deviation, plays an important role in analyzing the data by locating the data away from the center point of a specific data set.

In this blog, you will learn about what is the mean absolute deviation, the formula for mean absolute deviation, and how to find MAD with an example. 

Let’s first learn about what is M.A.D in Math.   

What is the Mean Absolute Deviation

Mean Absolute Deviation is a statistical term that tells how data is far from the center point of a given data set. It measures the average average distance between a specific data and the mean. The average absolute deviation summarizes a specific data set in one value. 

Mean Absolute Deviation Formula

The Mean Absolute Deviation Formula helps to calculate the mean value of the dispersion of the data. Meanwhile, data can be grouped or ungrouped. So, the M.A.D formula for grouped data and ungrouped will be different. 

You will learn the formula for both categories of data. 

M.A.D Formula for Grouped Data

The M.A.D formula for the grouped data is given as;

Where

• xi refers to the observation of a given data set.
• represents the mean of given data.
• n represents the total number of observations in a specific data set. 

MAD Formula for Ungrouped Data

The MAD Formula for ungrouped data is given as;

x_i refers to the observation of a given data set.

x is the mean of a data set.

f_i refers to the frequency of x_i

How to Find Mean Absolute Deviation– Steps 

You will learn about how to find mean absolute deviation of given data with examples. Here are the steps to help you in finding MAD. 

• First, calculate the mean of the given data.
• Find the distance between the mean and the data value by subtracting a number from the mean. It is called the absolute difference or absolute deviation.  
• Find the sum of absolute differences by adding them. 
• Divide the sum of absolute deviations by the total number of values in the data set.  

Let’s look at the finding mean absolute deviation example. 

Example 1: 

Find the mean absolute deviation for the given data set: 10, 12, 15, 22, 25, 28.

• First of all, we will find the mean of the data. Mean can be calculated by adding all values of the data and dividing it by the actual number of data. 

• Find the absolute difference. The absolute difference formula is,

So, we will calculate the absolute deviance for each value in the data. 

We have data 10, 12, 15, 22, 25, 28. The absolute deviance will be calculated as;

• Now, add the absolute deviance.

• Put the value in the formula

So, the MAD is 6

Example 2:

The table shows the number of students who remained absent each month. Calculate mean absolute deviation. 

To calculate MAD, we will follow the following steps.

1. Calculate the mean. 

Mean is 10.

• Find the absolute deviation of each value. 

• Get the sum of all absolute deviance.

• Divide the sum of absolute difference by the number of values in the data set.

So, the Mean Absolute Deviation is 2.6. 

Worksheet on Mean Absolute Deviation

MAD worksheets help students in mean absolute deviation practice problems. Here, we provide you with the worksheet on mean absolute deviation so that you can practice the problems and understand properly. 

• Find the Mean Absolute Deviation of 4, 3, 8, 9, and 7?
• calculate mean absolute deviation for the given data set. 8, 5, 6, 7, 10, 13, and 18.
• Sara found the following numbers in a survey. Calculate the M.A. D of these numbers 20, 18, 32, 45, 76, 56.  
• The marks of Erica in each subject is given below. Find the MAD for the given data. 

The speeds of different animals are mentioned below. Find the MAD.