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In this article we will discuss about the calculation of Mean Deviation (MD).
(MD or AD) The average value of the different deviations from the mean is a more accurate measure of variability. It is designated as Mean Deviation (MD) or Average Deviation (AD) or Mean Variation (MV). According to Garett, “The average deviation or AD (also written mean deviation or MD) is the mean of the deviations of all the separate scores in a series taken from their mean.”
The Formula for AD when scores are ungrouped is:
(average deviations when scores are ungrouped)
in which the bars |. | enclosing the x indicate that signs pre disregarded in arriving at the sum. As always, x is a deviation of a score from the mean, i. e., X- M=x.
Example:
Calculate the Mean Deviation of the following set of scores:
7,10,12,16,17,20,23.
Solution:
Sum of the scores or ∑x = 7 + 10+12+ 16+17 + 20 + 23= 105 105
Mean = 
AD = 32/7 = 4.57 (correct to two places of decimal).
Steps in Calculation of AD from Ungrouped Scores:
1. Find out the mean of series.
2. Find out x by using the formula: x = X – M.
3. Find out the sum of deviations or ∑|x| without taking the note of signs, and all deviations whether + or – should be treated as positive.
4. Divide |∑x| by N i.e., total number of cases.
5. Checking and reporting result.
Table III:
The Calculation of the Average Deviation or Mean Deviation from Data grouped into a frequency distribution mean (50) but of very different variability. Group A ranges from 20 to 80, and Group B from 40 to 60. Group A is three times as variable as Group B — spreads over three times the distance on the scale of scores-though both distributions have the same central tendency.
