The coefficient of mean deviation can be calculated by dividing the value of the mean absolute deviation by the mean of the data.
Coefficient of Mean Deviation = Mean Absolute Deviation/Mean.
Formula for Coefficient of Mean Absolute Deviation:
The value of the coefficient can be calculated using the formula,
Coefficient of Mean Deviation = Mean Absolute Deviation/Mean.
The Mean Absolute Deviation is given by the formula,
Mean Absolute Deviation = ∑|xi – X̄|/n.
Example 1:
Consider the set of data: 3, 3, 6, 7, 8, 9, 13.
Here, we have 7 data points therefore the value of n is 7. We first calculate the value of the mean for the given set of data values.
Mean = (3+ 3+ 6+ 7+ 8+ 9+ 13)/7 = 49/7 = 7.
We now calculate the value of the Mean Absolute Deviation as follows,
| xi | xi – X̄ = xi – 7 | |xi – X̄| |
| 3 | -4 | 4 |
| 3 | -4 | 4 |
| 6 | -1 | 1 |
| 7 | 0 | 0 |
| 8 | 1 | 1 |
| 9 | 2 | 2 |
| 13 | 6 | 6 |
| ∑|xi – X̄| = 18 |
Mean Absolute Deviation = ∑|xi – X̄|/n = 18/7 = 2.5714.
We now calculate the value of the coeffcient of mean deviation as follows,
Coefficient of Mean Deviation = Mean Absolute Deviation/Mean = 2.5714/7 = 0.3673.
Example 2:
Consider the following set of data: 16, 39, 45, 46, 49, 99.
Mean = (16+ 39 + 45+ 46+ 49 + 99)/6 = 49.
| xi | xi – X̄ = xi – 49 | |xi – X̄| |
| 16 | -33 | 33 |
| 39 | -10 | 10 |
| 45 | -4 | 4 |
| 46 | -3 | 3 |
| 49 | 0 | 0 |
| 99 | 50 | 50 |
| ∑|xi – X̄| = 100 |
Mean Absolute Deviation = 110/6 = 16.6667
Coefficient of Mean Deviation = Mean Absolute Deviation/Mean = 16.6667/49 = 0.3401.
