Mean Deviation

• Definition: Mean deviation measures the average deviation of data points from a central point, usually the mean or median.
• Formula: =

     

   ​, where xi​ are individual data points, a is the central value (mean or median), and n is the number of observations.
• Calculation: It uses absolute deviations to avoid cancellation of positive and negative deviations around the mean.
• Use: Provides a measure of dispersion that includes all data points, but is less sensitive to outliers compared to standard deviation.

Example

Let’s say you have the dataset:
Data = [2, 4, 6, 8, 10]

• Mean = (2 + 4 + 6 + 8 + 10) / 5 = 6
• Deviations from mean = [4, 2, 0, 2, 4]
• Mean deviation = (4 + 2 + 0 + 2 + 4) / 5 = 2.4

This tells you that on average, each number is 2.4 units away from the mean.