An absolute measure of dispersion: The measures which express the scattering of observation in terms of distances i.e., range, quartile deviation. The measure which expresses the variations in terms of the average of deviations of observations like mean deviation and standard deviation.

Measure of Dispersion Based on Absolute Deviation:

One measure of dispersion that is based on absolute deviation is the Mean Absolute Deviation (MAD). The MAD is a statistical measure that calculates the average absolute deviation of data points from the mean of a data set. It provides a measure of how spread out the data points are from the mean.

Formula for Mean Absolute Deviation (MAD):
MAD = Σ |Xi - X̄| / n

Where:
- MAD is the Mean Absolute Deviation
- Σ represents the sum of all terms
- Xi represents each individual data point
- X̄ represents the mean of the data set
- n represents the number of data points in the data set

Calculating the Mean Absolute Deviation (MAD):
To calculate the MAD, follow these steps:
1. Calculate the mean (X̄) of the data set.
2. For each data point, calculate the absolute deviation by subtracting the mean from the data point and taking the absolute value.
3. Sum up all the absolute deviations.
4. Divide the sum of absolute deviations by the number of data points to get the MAD.

Interpretation of Mean Absolute Deviation (MAD):
The MAD provides a measure of the average distance between each data point and the mean of the data set. A smaller MAD indicates that the data points are closer to the mean and less spread out, while a larger MAD indicates that the data points are further away from the mean and more spread out.

Advantages of Mean Absolute Deviation (MAD):
- MAD is easy to understand and calculate.
- It uses absolute values, which eliminates the issue of positive and negative deviations canceling each other out.
- It provides a measure of dispersion that is based on the absolute deviation of data points from the mean, which can be useful in certain situations.

Limitations of Mean Absolute Deviation (MAD):
- MAD does not take into account the squared deviations, which can be problematic in some statistical analyses.
- MAD gives equal weight to all data points, which may not accurately reflect the importance or significance of each data point.
- MAD is sensitive to extreme values or outliers as it considers the absolute distance from the mean, which can be misleading in some cases.

In conclusion, the Mean Absolute Deviation (MAD) is a measure of dispersion based on absolute deviation. It calculates the average absolute deviation of data points from the mean of a data set. While MAD has its advantages and limitations, it can provide valuable insights into the spread or variability of data.