Mean Deviation, also known as Average Deviation, is a statistical measure of dispersion that shows the average distance of each data point from a central value such as the mean, median, or mode. It provides a clearer idea of variability in a dataset than simple measures like range.
Definition
Mean Deviation is the arithmetic average of the absolute deviations of values from a measure of central tendency (typically the mean or median).
Formulas
For Ungrouped Data:
MD (about Mean) = (Σ|X − Mean|) / N
MD (about Median) = (Σ|X − Median|) / N
For Grouped Data:
MD = (Σf|X − A|) / Σf
Where:
X = Midpoint of the class
A = Mean or Median
f = Frequency of the class
Coefficient of Mean Deviation:
Coefficient = MD / Central Value
Example: MD / Mean or MD / Median
Step-by-Step Example (Ungrouped Data)
Data: 6, 8, 10, 12, 14
- Calculate the Mean: (6 + 8 + 10 + 12 + 14) / 5 = 10
- Find absolute deviations: |6−10|=4, |8−10|=2, |10−10|=0, |12−10|=2, |14−10|=4
- Sum of deviations: 4 + 2 + 0 + 2 + 4 = 12
- Mean Deviation = 12 / 5 = 2.4
- Coefficient = 2.4 / 10 = 0.24
Step-by-Step Example (Grouped Data)
| Class Interval | Frequency (f) | Midpoint (X) | |X − Mean| | f × |X − Mean| |
|---|---|---|---|---|
| 0-10 | 4 | 5 | 5 | 20 |
| 10-20 | 6 | 15 | 5 | 30 |
| 20-30 | 10 | 25 | 5 | 50 |
Total frequency = 20
Σf|X − Mean| = 100
Mean Deviation = 100 / 20 = 5
Merits of Mean Deviation
- Based on all values of the data
- Less affected by extreme values than standard deviation
- Simpler to calculate and understand
- Useful for comparing variability across datasets
Demerits of Mean Deviation
- Ignores signs by using absolute values, losing direction of deviation
- Not suitable for algebraic operations or further statistical analysis
- Less commonly used in advanced statistical methods
Comparison with Other Measures
| Measure | Basis | Affected by Outliers | Mathematical Use |
|---|---|---|---|
| Range | Extreme values | Highly | No |
| Quartile Deviation | Middle 50% | Less | Limited |
| Mean Deviation | All values (absolute) | Moderately | Limited |
| Standard Deviation | All values (squared) | Highly | Yes |
Applications of Mean Deviation
- Business and economic studies comparing market stability
- Social sciences for measuring variability in surveys
- Educational statistics to analyze exam score consistency
Conclusion
Mean Deviation is a practical and accessible measure of dispersion, offering a middle ground between simplicity and meaningful analysis. It is especially useful when a dataset's variability needs to be assessed around a central value, particularly in descriptive studies. While it may not be suitable for complex statistical modeling, it remains highly relevant for UGC NET Commerce preparation.