Mean Deviation
The two methods of dispersion namely range and quartile deviation is not measure of dispersion in the strict sense of term, they do not show the slatterns around an average. However, to study the formation of a distribution we must take the deviations from an average. The other two measures namely the average deviation & the standard deviation help us in achieving this goal. The mean deviation is also termed as the average deviation. This is the average difference between the items in distributing and the median or mean of that series. Theoretically there is a merit in taking the deviations from median as the sum of deviation of item from median is minimum, when the signs are ignored. In practice the arithmetic mean is most frequently used in calculating the value of average deviation and this is the reason why it is more commonly known men deviation. In any of the case the average used must be clearly stated in a given problem, so that any possible confusion in the meaning is avoided.
Computation of mean deviation-individual observations
If X2 X1 X3 XN are N given observation then the deviation about an average A is given by
M.D. = 1/n Σ| X - A |
1/N Σ |D| or Σ | D| / N
Where |D| = X - A | read as mod (X-A) is the modulus value or absolute value of the deviation ignoring plus and minus signs.
Coefficient of M>D = M>D / median
Illustration:
Calculate the mean deviation & its coefficient of the two income groups of living and seven members given below:
|
I ($)
|
4000
|
4200
|
4400
|
4600
|
4800
|
|
|
|
II ($)
|
3000
|
4000
|
4200
|
4400
|
4600
|
4800
|
5800
|
Solution:
Calculation of mean deviation
|
|
Deviation from median 4400 |D|
|
|
Deviation from median 4400 |D |
|
|
4000
|
400
|
3000
|
1400
|
|
4200
|
200
|
4000
|
400
|
|
4400
|
0
|
4200
|
200
|
|
4600
|
200
|
4400
|
0
|
|
4800
|
400
|
4600
|
20
|
|
|
|
4800
|
400
|
|
|
|
5800
|
1400
|
|
N=5
|
Σ | D| = 1200
|
N+7
|
Σ|D| = 4,000
|
Mean deviation group; M.D = Σ|D|/N
|D| = deviation from median ignoring signs,
Median = size of N+1 / 2 th item = 5+1 / 2 = 3rd item
Size of 3rd item is 4,400 M.D = 1,200 / 5 = 240
This means that the average deviation of the individual incomes from the median income is $ . 240.
Mean deviation group
Mean = size of N+1 / 2 th item = 7+1 / 2 = 4th item
Size of 4th item is 4,400
Σ |D| = 4,000, N = 7
M.D = 4,000 / 7 = 571.43.
Coefficient of M.D = 240 / 4,400 = 0.054
and for the second group
Coefficient of M.D = 571.43 / 4,400 = 0.130.