The coefficient of mean deviation is a relative measure of dispersion that gives us information about the amount of “variability” present in our data. If the value of the coefficient of mean deviation is high then we can say that the data has a greater spread. If the value of the coefficient is low then it means that there is a lesser degree of variability in the given data. The coefficient of mean deviation can be calculated by dividing the value of the mean absolute deviation by the mean of the data.
Formula for Coefficient of Mean Absolute Deviation:
The value of the coefficient can be calculated using the formula, \text{Coefficient of Mean Deviation }= \frac{\text{Mean Absolute Deviation}}{\text{Mean}(\bar{x})} where, the Mean Absolute Deviation is given by the formula,\text{Mean Absolute Deviation }= \frac{\sum_{i} |x_i - \bar{x} |}{n}
Example 1:
Consider the following 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. \bar{x} = \frac{\sum_{i} x_i}{n} = \frac{3+ 3+ 6+ 7+ 8+ 9+ 13}{7}. \bar{x} =\frac{49}{7} = 7. We now calculate the value of the Mean Absolute Deviation as follows,
| x_i | x_i-\bar{x} = x_i - 7 | |x_i-\bar{x}| |
| 3 | -4 | 4 |
| 3 | -4 | 4 |
| 6 | -1 | 1 |
| 7 | 0 | 0 |
| 8 | 1 | 1 |
| 9 | 2 | 2 |
| 13 | 6 | 6 |
| \sum_i |x_i-\bar{x}| = 18 |
\text{Mean Absolute Deviation }= \frac{\sum_{i} |x_i - \bar{x} |}{n} = \frac{18}{7} \text{Mean Absolute Deviation }= 2.5714 We now calculate the value of the coeffcient of mean deviation as follows, \text{Coefficient of Mean Deviation }= \frac{\text{Mean Absolute Deviation}}{\text{Mean}(\bar{x})} = \frac{2.5714}{7} = 0.3673
Example 2:
Consider the following set of data: 16, 39, 45, 46, 49, 99. \bar{x} = \frac{\sum_{i} x_i}{n} = \frac{16+ 39 + 45+ 46+ 49 + 99}{6}. \bar{x} =\frac{294}{6} = 49.
| x_i | x_i-\bar{x} = x_i - 49 | |x_i-\bar{x}| |
| 16 | -33 | 33 |
| 39 | -10 | 10 |
| 45 | -4 | 4 |
| 46 | -3 | 3 |
| 49 | 0 | 0 |
| 99 | 50 | 50 |
| \sum_i |x_i-\bar{x}| = 100 |
\text{Mean Absolute Deviation }= \frac{\sum_{i} |x_i - \bar{x} |}{n} = \frac{100}{6} = 16.6667 We now calculate the value of the coeffcient of mean deviation as follows, \text{Coefficient of Mean Deviation }= \frac{\text{Mean Absolute Deviation}}{\text{Mean}(\bar{x})} = \frac{16.6667}{49} = 0.3401.
