Mean Absolute Deviation Calculator

MAD Calculator

Mean Absolute Deviation Calculator is an easy-to-use online tool to compute MAD quickly for any dataset. It helps users avoid the manual, time-consuming process of calculating deviations.

This MAD Calculator instantly displays the result, showing the MAD, sample size, mean, and other helpful metrics like the sum of absolute differences. 

What is the Mean Absolute Deviation?

Mean Absolute Deviation (MAD) is a statistical measure that represents the average between each data point and the mean of the dataset. Unlike standard deviation, MAD does not square the differences, making it less sensitive to extreme values. 

It provides information about the variability of the dataset values and shows the separation of the data values around the mean. This straightforward way helps to understand the variability of data or how much data points deviate from the average. 

Mean Absolute Deviation Formula

The formula for mean absolute deviation is:

Breakdown of given terms:

• N = Number of data points
• xi = Individual data point
• x̄ = Mean of the data set
• |xi - x̄| = Absolute differences between the data point and the mean

How to Find Mean Absolute Deviation?

To find the average absolute deviation value with the MAD formula follow the below manual steps.

• First, calculate the mean (average) of the data set by summing all data values and dividing it with the total number of elements. To find the quick mean value, use our Mean Calculator.
• Secondly, subtract the mean from each data point and take the absolute value for each result.  
• Finally, sum up all the absolute deviations and divide the number of observations to get the MAD value by using the MAD formula. 

Alternatively, use our Mean Absolute Deviation (MAD) calculator to get quick and accurate results without following any manual steps. 

Mean Absolute Deviation Example

Here, we will solve the manual example without the help of a mean absolute deviation calculator. It helps to understand the concept of the calculation of mean absolute deviation value by using the MAD formula.

Example: If the data value is {13, 23, 12, 44, 23, 55}, then Calculate the MAD-value for the given dataset by using the MAD formula.

Solution:

Step 1: First, evaluate the mean of the given data values with the mean formula.

Mean  = (13 + 23 + 12 + 44 + 23 + 55) / 6

=170 / 6 

=28.333

Step 2: Now, take the difference of each data value by the mean of data to find the absolute deviation value.

Step 3: Find the MAD value by putting the above values in the mean absolute deviation formula.

MAD = 84.666 / 6

MAD = 14.111

Frequently Asked Questions

What is the purpose of mean absolute deviation?

The Mean Absolute Deviation (MAD) is used to measure the variability or dispersion of a dataset. It finds the average distance of each data point from the mean and provides information about the separation of the data values.

What is the difference between MAD and standard deviation?

Both are used to measure data variability or dispersion value around the mean of any data. MAD is similar to standard deviation but uses absolute values instead of squares. However, standard deviation uses the sum of squares and shows the differences in variability.

Can this calculator work for both small and large datasets?

Yes, our MAD calculator handles datasets of any size, from small samples to large population data. Due to this, it proved a helpful tool for various types of data analysis to measure variability.

What does the high or low MAD value represent?

A high MAD value shows data points are more spread from the mean which causes the reason for high variability. A low MAD value means data points are closer to the mean and show lower variability or greater consistency in the dataset.

Can mean absolute deviation is negative?

No, mean absolute deviation (MAD) cannot be negative. Because MAD is the absolute value of the difference of data values from the mean and absolute values are always non-negative.