Mean Absolute DeviationMean deviation or mean absolute deviation for a set of values is the arithmetic mean of the absolute values of all the deviations taken from its central value.
Mean deviation from the mean for individual observations is given by:
text{M}.text{D.}=frac{sum mid x_i-overline{x}mid}{n},
where n is the number of data values, x_i are the data values, and overline{x} is the mean.
If all the data values are constant, then the mean deviation is zero.Mean deviation takes on minimum values when the deviations are taken from the median.Mean deviation remains unchanged due to change of origin but is affected due to change of scale.
Example: Find the mean absolute deviation for Kadie's biology quiz scores: 16, 15, 20, 19, 13, 19. Scores are out of 20 points.
Solution: Find the average, overline{x}, of the scores: overline{x} =frac{16+15+20+19+13+19}{6} =17
Let's look at the table we will need for the problem: List the data in the left column, the mean in the center column, and the absolute value of their difference in the last column.
To find the mean absolute variation, find the sum of the values in the last column and then divide by the number of data values.
text{M}.text{D}=frac{sum mid x_i-overline{x}mid}{n}=frac{4+2+1+2+2+3}{6}=frac{14}{6} = 2.overline{333}