- 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.![\[[= \frac{\sum_{i=1}^{n} (x_i - a)}{n}]\]](data:image/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg== "Rendered by QuickLaTeX.com")
- 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.
![\[[= \frac{\sum_{i=1}^{n} (x_i - a)}{n}]\]](https://bbaguru.in/wp-content/ql-cache/quicklatex.com-372b15409e268eadd5a9bb0550e777f0_l3.png "Rendered by QuickLaTeX.com")
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.