Many students have some confusion about the concept of mean deviation and often confuse it with standard deviation. In this article, you will learn more about this metric and how to obtain it with our online mean deviation calculator.
Average Deviation (Mean Absolute Deviation) Calculator
What is the mean absolute deviation?
The mean absolute deviation, also known as average deviation, is a measure of dispersion obtained by calculating the mean of the absolute values of the difference between the observed and expected value of a set of data.
Mathematically it is expressed as follows:
Where:
- Dm: Mean absolute deviation.
- x̄: Mean.
- N: Number of evaluated values.
- xi: Each one of the values.
Mean Absolute Deviation vs. Standard Deviation
Mean absolute deviation, like standard deviation, are measures of dispersion; however, the standard deviation is calculated using the squares of the difference of the observed values from their mean. When squared, it becomes a more sensitive metric to outliers, making it more appropriate than the average deviation for evaluating a data set.
How to use the average deviation calculator?
The use of the application is straightforward; you only have to follow the following steps:
- Choose between the options for the decimal separator and the data separator.
- Indicate the values of the data set.
- Click on Solve.
- Immediately, you will be able to visualize the calculation procedure step by step.
An example is shown below:
Example of calculating the mean deviation
For the following data, calculate the mean absolute deviation:
3, 5, 8, 6, 2, 4, 7, 5
Solution
We enter the data in the calculator:
When clicking on Solve, we will obtain the following:
Average Deviation: 1.5
Mean: 5
Count of Data: 8
According to the data of the problem we have:
- Σxᵢ = 40
- NÂ =Â 8
- x̄ = 40/8 = 5
| xi | xi – xÌ„ | |xi – xÌ„| |
|---|---|---|
| 3 | -2 | 2 |
| 5 | 0 | 0 |
| 8 | 3 | 3 |
| 6 | 1 | 1 |
| 2 | -3 | 3 |
| 4 | -1 | 1 |
| 7 | 2 | 2 |
| 5 | 0 | 0 |
| Σxáµ¢ = 40 | xÌ„ = 40/8 = 5 | Σ|xáµ¢ – xÌ„| = 12 |
Finally, we calculate the average deviation:
You can also calculate other measures of dispersion or central tendency using the following options:
- Standard Deviation Online Calculator.
- Variance online application.
- Online calculator for mean, median, mode, and range.
Final Reflection
In short, our mean deviation calculator finds the average of the absolute deviations of the values from the mean in a series of ungrouped data. We are sure it will help you make your homework more accessible and faster.
