Mean Absolute Deviation Calculator

The mean absolute deviation formula helps in calculating mean absolute deviation (MAD), which is the average of the absolute deviation (distance) of the data points from the mean of the data set.

What is Mean Absolute Deviation Calculator?

'Mean Absolute Deviation Calculator' is an online tool that helps to calculate the mean absolute deviation for a given data. Online Mean Absolute Deviation Calculator helps you to calculate the mean absolute deviation for a given data in a few seconds.

Mean Absolute Deviation Calculator

NOTE: Enter values, separated by a comma.

How to Use Mean Absolute Deviation Calculator?

Please follow the steps below on how to use the calculator:

• Step 1: Enter the numbers separated by a comma in the given input box.
• Step 2: Click on the "Calculate" button to find the mean absolute deviation for a given data.
• Step 3: Click on the "Reset" button to clear the fields and find the mean absolute deviation for the different numbers.

How to Find Mean Absolute Deviation?

Mean Absolute deviation is defined as the average deviation of the data points from a center point. 

Mean absolute deviation = ∑(|x_i - x|) / N

Where x_i is individual values in the sample, and x is the mean or an average of the sample, N is the number of terms in the sample.

The mean value or average of a given data is defined as the sum of all observations divided by the number of observations. The mean is calculated using the formula:

Mean or Average(x) = (x₁ + x₂ + x₃...+ x_n) / n

Where n = total number of terms, x₁, x₂, x₃, . . . , x_n = Different n terms

Solved Examples on Mean Absolute Deviation Calculator

Example 1:

Find the Mean absolute deviation for the following set of data: {51,38,79,46,57} and verify it using the online mean absolute deviation calculator.

Solution:

Given N = 5

Mean absolute deviation = ∑(|x_i - x|) / N

Mean(x) = 51 + 38 + 79 + 46 + 57 / 5 = 54.2

Mean absolute deviation = (|51 − 54.2|) + (|38 − 54.2|) + (|79 − 54.2|) + (|46 − 54.2|) + (|57 − 54.2|) / 5

= 11.04

Therefore, the mean absolute deviation is 11.04

Example 2:

Find the Mean absolute deviation for the following set of data: {1, 6, 7, 2, 9} and verify it using the online mean absolute deviation calculator.

Solution:

Given N = 5

Mean absolute deviation = ∑(|x_i - x|) / N

Mean(x) = 1 + 6 + 7 + 2 + 9 / 5 = 5

Mean absolute deviation = (|1 - 5|) + (|6 - 5|) + (|7 - 5|) + (|2 - 5|) + (|9 - 5|) / 5

= 2.8

Therefore, the mean absolute deviation is 2.8

Example 3:

Find the Mean absolute deviation for the following set of data: {4, 8, 11, 19} and verify it using the online mean absolute deviation calculator.

Solution:

Given N = 4

Mean absolute deviation = ∑(|x_i - x|) / N

Mean(x) = 4 + 8 + 11 + 19 / 4 = 42/4 = 10.5

Mean absolute deviation = (|4 - 10.5|) + (|8 - 10.5|) + (|11 - 10.5|) + (|19 - 10.5|) / 4

= 4.5

Therefore, the mean absolute deviation is 4.5

Similarly, you can try the online mean absolute deviation calculator to find the mean absolute deviation for the following data sets:

• 21,14,16,8,2,4,15,8
• 25,1,7,15,6,14,14,25,7

☛ Related Articles:

• Standard Deviation
• Mean

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