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Mean Deviation from the Mean


Consider the observations 3, 5, 6, 7, 9.
A.M =

Let us find the deviations of the individual items from the mean. They are 3, 1, 0, 1, 3 respectively. Sum of these deviations is zero, thus finding the mean derivative about the mean will result in zero and therefore is not of any use to us as far as measure of dispersion is concerned.

Mean deviation about the mean is the average of all the deviation from the mean

Mean of deviations =

So instead of taking the actual deviations, we consider the absolute deviations of these observations from there mean.

i.e. absolute deviations from the mean are 3, 1, 0, 1, 3 ; their sum = 8.

M.D (from mean) =

Definition (Mean Deviation)


Let be values. The mean deviation about the mean of these values is given by M.D = when is the mean of the values.

Note:
  1. Mean deviation can be calculated about any fixed quantity. Mean deviation about 'a' will be .
  2. It the mean deviation is calculated about the median M, then it is
Example 1. Find the mean deviation about the mean for the following data.
18, 20, 12, 14, 19, 22, 26, 16, 19, 24

Solution:

 =
Mean deviation about the mean =

Example 2:
Find the mean deviation about the median for the following data: 29, 31, 35, 37, 55, 63, 72

Solution:
n = 7
Arrange data in ascending order
Note: It already is in ascending order.
29, 31, 35, 37, 55, 63, 72
Median is the middle reading = 37 = M.
Absolute deviations from the median are 8, 6, 2, 0, 18, 26, 35
sum of absolute deviations = 95
Mean deviation about M =  = 13.57




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