Want to find the mean absolute deviation instead? Use the mean absolute deviation calculator.
How to Use the Median Absolute Deviation Calculator
This calculator helps you find the median absolute deviation of a dataset with a click of a button. To use the calculator:
- Enter your data values in the input box. You can separate the values using commas, spaces, tabs, or line breaks. The calculator also allows you to copy-paste values directly from Excel, Google Sheets, or text documents.
- Click Calculate.
The calculator will instantly return the median absolute deviation for your dataset. It also provides a clear, step-by-step solution to help you learn how to compute the value using your own dataset.
What Is Median Absolute Deviation?
Median absolute deviation is a measure of spread that tells you how far the values in a dataset typically are from the median.
It is called “median absolute deviation” because the calculation uses:
- the median as the center of the dataset,
- the absolute deviations from that median,
- and the median of those deviations as the final answer.
In simple terms, the median absolute deviation tells you the typical distance between the data values and the middle value of the dataset. Median absolute deviation is especially useful when a dataset has outliers or is skewed because it is based on medians instead of means.
Median Absolute Deviation Formula
The median absolute deviation formula is: MAD = median(|xᵢ − median(x)|)
Where:
- MAD is the median absolute deviation.
- xᵢ is each value in the dataset.
- median(x) is the median of the dataset.
- |xᵢ − median(x)| is the absolute deviation of each value from the median.
Note. Our median absolute deviation calculator uses the classical unscaled formula as defined above. This means that it returns the median of the absolute deviations without multiplying by a scaling constant.
In some statistical software, the median absolute deviation is multiplied by 1.4826 as a scaling factor to make it a robust estimate of the standard deviation of the dataset. Therefore, when using our calculator, keep in mind that the solution you get is based on the direct median absolute deviation formula, which is mainly taught to students.
How to Calculate Median Absolute Deviation
To calculate the median absolute deviation manually:
- Find the median of the dataset.
- Find the absolute deviation of each value from the median.
- Find the median of the absolute deviations to get the median absolute deviation.
Example
Find the median absolute deviation of the following dataset:
15, 10, 22, 12, 100, 14, 18
Solution
To find the median absolute deviation of the above dataset by hand, follow these steps:
Step 1: Find the median of the dataset.
By definition, the median is the value at the middle of a sorted dataset. Therefore, to find the median, we sort the data in ascending order as follows: 10, 12, 14, 15, 18, 22, 100
Since the number of observations is odd (n = 7), the median is the value in the (n+1)/2 position. Therefore, the median is the value in the 4th position of the ordered data.
Hence, Median = 15.
Need to learn more about the median? Use the median calculator to get instant results, with a clear, step-by-step explanation.
Step 2: Find the absolute deviation of each value from the median.
By definition, the absolute deviation from the median formula is: |xᵢ − median|
Now, using median = 15, we get
|10 − 15| = 5
|12 − 15| = 3
|14 − 15| = 1
|15 − 15| = 0
|18 − 15| = 3
|22 − 15| = 7
|100 − 15| = 85
Therefore, the absolute deviations are:
5, 3, 1, 0, 3, 7, 85
Step 3: Find the median of the absolute deviations.
To find the median of the absolute deviations, we first arrange these deviations in ascending order and find the value at the 4th position.
Arranging these deviations in ascending order, we have: 0, 1, 3, 3, 5, 7, 85
The value at the 4th position is 3. Therefore, the median absolute deviation is 3. This means the typical distance from the median is 3 units.
Note. The extreme value (100) does not influence the result. This explains why median absolute deviation is useful when working with data with outliers and extreme values.
When to Use Median Absolute Deviation?
The median absolute deviation is appropriate when:
- your dataset contains extreme values,
- the data are skewed,
- the median is a better center than the mean,
- you want a robust measure of variability,
- you are comparing the typical distance from the median,
- or you are working with data where standard deviation may be too sensitive.
Median Absolute Deviation vs Mean Absolute Deviation
Median absolute deviation and mean absolute deviation are related, but they are not the same. While the median absolute deviation measures distances from the median, the mean absolute deviation measures distances from the mean. Therefore, if you need the average distance from the mean instead, you should use the mean absolute deviation calculator.
Frequently Asked Questions
It calculates the median absolute deviation of a dataset and shows the step-by-step solution.
Median absolute deviation is a measure of spread found by taking the median of the absolute deviations from the median of a dataset.
The formula is: MAD = median(|xᵢ − median(x)|), where MAD is the median absolute deviation, xi are the individual data values, and median (x) is the median of the original dataset.
No, the Median Absolute Deviation (MAD) is not heavily affected by outliers because it relies on the median rather than the mean. Therefore, it is considered a highly robust measure of statistical dispersion.
No. Median absolute deviation uses the median as the center and takes the median of the absolute deviations. On the other hand, the mean absolute deviation uses the mean as the center and takes the average of the absolute deviations.
No. This calculator returns the classical unscaled median absolute deviation.
