4.11:
Mean Absolute Deviation
The mean absolute deviation provides the absolute value of the average difference between the data values and the mean.
It is calculated as the sum of the absolute deviations from the mean divided by the sample size.
For example, three students have three, five, and seven cookies in their lunch boxes. The deviations in the number of cookies from the mean of five cookies are minus 2, zero, and two.
If one adds these deviations, the positive and negative values cancel each other out, giving a zero mean deviation, which is unhelpful. If the absolute values are added, one obtains a single non-zero value instead.
This value, when divided by the sample size, gives the mean absolute deviation.
Calculating the mean absolute deviation involves a non-algebraic modulus operation, while the standard deviation uses algebraic operations. Therefore it is not suitable for inferential statistics.
It is also a biased statistic, as the calculated mean absolute deviation of a sample does not adequately represent the population mean absolute deviation.
4.11:
Mean Absolute Deviation
The mean absolute deviation is also a measure of the variability of data in a sample. It is the absolute value of the average difference between the data values and the mean.
Let us consider a dataset containing the number of unsold cupcakes in five shops: 10, 15, 8, 7, and 10. Initially, calculate the sample mean. Then calculate the deviation, or the difference, between each data value and the mean. Next, the absolute values of these deviations are added and divided by the sample size to obtain the mean absolute deviation.
In the above data set, the obtained mean is 10. The deviations from the mean are 0, 5,-2,-3, and 0. The absolute values of these deviations are 0,5,2,3, and 0. Upon adding these, we get a sum of 10. Upon dividing ten by the sample size, we get a value of 5, which is the mean absolute deviation.
It is noteworthy that the mean absolute deviation is computed using absolute values, so it involves using a non-algebraic operation. Hence, the mean absolute deviation cannot be used in inferential statistics, which involves using algebraic operations.
Furthermore, the mean absolute deviation of a sample is biased, as it doesn’t adequately represent the mean absolute deviation of a population.