Mean deviation

Mean deviation is the measure of dispersion that is based on the absolute deviations only. It is also known as the average deviation or the mean absolute deviation. This statistical measure represents the average absolute difference between each value in a set of data and the mean of that set.

Formula
The formula for mean deviation is as follows:

Mean deviation = Σ |X - X̄| / n

Where,
Σ = Summation
X = Each value in the data set
X̄ = Mean of the data set
n = Number of values in the data set

Interpretation
The mean deviation provides an idea of how much variation there is in a set of data. A smaller mean deviation indicates that the data points are closer to the mean, while a larger mean deviation indicates that the data points are more spread out.

Advantages and disadvantages
Advantages of mean deviation include its simplicity and ease of calculation. It is also less sensitive to extreme values than other measures of dispersion, such as standard deviation. However, it is less commonly used in statistical analysis compared to other measures of dispersion.

Conclusion
In summary, mean deviation is a measure of dispersion based on the absolute deviations only. It represents the average absolute difference between each value in a set of data and the mean of that set. While it has its advantages and disadvantages, it can provide valuable insights into the variation of a data set.