The Mean Absolute Deviation (MAD) Calculator measures the average distance between data points in a set and their mean. It’s a crucial statistical tool used across various fields to understand the variability or dispersion within a dataset.
Formula of Mean Absolute Deviation Calculator
The formula for MAD is:
MAD = Σ |Xi – X̄| / n
Where:
- MAD: Represents the mean absolute deviation.
- Σ: Denotes the sum of the absolute differences for all data points.
- Xi: Stands for each individual data point.
- X̄: Represents the mean (average) of the dataset.
- |Xi – X̄|: Is the absolute difference between each data point and the mean.
- n: Signifies the total number of data points in the set.
Example of Mean Absolute Deviation Calculator
Let’s illustrate this with a step-by-step example using a dataset [10, 15, 20, 25, 30].
- Calculate the Mean (X̄): X̄ = (10 + 15 + 20 + 25 + 30) / 5 = 100 / 5 = 20.
- Calculate the Absolute Differences for Each Data Point:
- |10 – 20| = 10
- |15 – 20| = 5
- |20 – 20| = 0
- |25 – 20| = 5
- |30 – 20| = 10
- Sum Up the Absolute Differences: 10 + 5 + 0 + 5 + 10 = 30.
- Divide the Sum by the Total Number of Data Points (n): MAD = 30 / 5 = 6.
Useful References and Tables
Below is a table summarizing general terms related to MAD calculations:
| Term | Description |
|---|---|
| Variability | Measure of data spread |
| Deviation | Distance between a value and mean |
| Dispersion | Degree of dataset’s variability |
| Standard Deviation | Measure of data spread |
This table can help individuals understand and interpret the results without needing to perform calculations every time.
Most Common FAQs
A: MAD measures the average distance between each data point and the mean, indicating the variability or dispersion within the dataset. Higher MAD values suggest greater variability.
A: Both measure dispersion, but while standard deviation squares the differences from the mean, MAD considers absolute differences, making it simpler to compute but less sensitive to extreme values.
